Теория хаоса — математический аппарат, описывающий поведение некоторых нелинейных динамических систем, подверженных при определённых условиях явлению, известному как хаос (динамический хаос, детерминированый хаос). Поведение такой системы кажется случайным, даже если модель, описывающая систему, является детерминированной. Для акцентирования особого характера изучаемого в рамках этой теории явления, обычно принято использовать название: теория динамического хаоса.
New York: Springer, 1997. — 251 p.
This book is a visual introduction to chaos and bifurcations in noninvertible discrete dynamical systems in two dimensions, using the method of critical curves.
Springer International Publishing, Switzerland, 2016. – 276 p. – ISBN10: 3319287621 Presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, nonlinear dynamics in fluid and thermal dynamics, nonlinear geophysical dynamics, time-delay, and bio-network dynamics Analyzes methods for discontinuous dynamical systems Examines...
American Mathematical Society, International Press, 2002. — 361 p. This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of 'physical' intuition while staying mathematically rigorous. In addition, they...
IOP Publishing Ltd, 2025. — 356 p. — ISBN-13 978-0750351607 Ultra Poincaré chaos offers an alternative to Lorenz chaos, showcasing alpha unpredictability, which is a characteristic of an isolated motion. Alpha labeling is a valuable mathematical structure for studying complexity, as well as for the entirety of dynamical systems theory. Additionally, unique historical and...
New York: Springer, 2016. - 457p.
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can...
Springer, 2020. — 233 p. — (Nonlinear Systems and Complexity 29). — ISBN: 978-3-030-35853-2. The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an...
Berlin, New York: Springer, 2005 — 352 p. — ISBN10: 3540286101; ISBN13: 978-3540286103. Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society . The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme...
De Gruyter, 2023. — 214 p. Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities,...
ITexLi, 2024. — 79 p. — ISBN 1837681236 9781837681235 1837681228 9781837681228 1837681244 9781837681242. This volume provides a comprehensive overview of chaos theory. It includes chapters that discuss the history and development of chaos theory, the effectiveness of a chaos auto-associated model based on the Chebyshev-type activation function, neurite morphology, chemical...
N.-Y.: Springer, 2015. - 865p.
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are...
Springer, 2010. — 413 p. — ISBN-13 978-3642066573 Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase...
Singapore: World Scientific, 2016. — 576 p. This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems...
World Scientific Publ., 2003. — 563 p. — (World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 45). — ISBN: 978-238-459-6. This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators,...
Boca Raton: CRC Press / Taylor & Francis, 2013. — 234 p. For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications...
Singapore: World Scientific, 2000. — 164 p. — ISBN: 9789810233280, 9810233280. Aimed at mathematicians and mathematical physicists, this text demonstrates how the powerful technology of transfer operators, imported from statistical physics, has been used to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic...
Springer, 2011. — 358 p. — (Understanding Complex Systems). — ISBN: 9783642219214. Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and...
Berlin: Springer, 2013. - 296p. Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative...
New York: Springer, 2015. - 304 p. Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever...
Berlin: Springer, 2012. - 270p. Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the...
Springer, 2014. - 201 pp. The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of...
Naval Postgraduate School, Monterey, CA, 1991. — 170 p. The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to...
Cambridge University Press, 1993. — 306 p. — (Cambridge Nonlinear Science Series 4). — ISBN-13 9780521484510. This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterize chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and...
Translated by Ian Stewart. — New York: Cambridge University Press, 1998. — 410 p. — ISBN 978-0-521-36025-8. As a mathematician one is accustomed to many things. Hardly any other academics encounter as much prejudice as we do. To most people, mathematics is the most colourless of all school subjects - incomprehensible, boring, or just terribly dry. And presumably, we...
4. Auflage. — Vieweg, 1992. — 390 s. — ISBN: 978-3-528-34461-0. Oft wird heute im Zusammenhang mit der "Theorie komplexer dynamischer Systeme" von einer wissenschaftlichen Revolution gesprochen, die in alle Wis senschaften ausstrahlt. Computergrafische Methoden und Experimente bestim men heute die Arbeitsweise eines neuen Teilgebietes der Mathematik: der "experimentellen...
Springer, 1998. — 435 p. Proceedings of a Workshop Held in Carry-Le Rouet, France, 16–21 June 1997. Over the last few years it has become apparent that fluid turbulence shares many common features with plasma turbulence, such as coherent structures and self-organization phenomena, passive scalar transport and anomalous diffusion. This book gathers very high level, current papers...
Philadelphia: American Mathematical Society, 1997. - 180 p.
This book presents the study of ergodic properties of so-called chaotic dynamical systems. One of the central topics is the interplay between deterministic and quasi-stochastic behavior in chaotic dynamics and between properties of continuous dynamical systems and those of their discrete approximations. Using simple...
Cambridge University Press, New York, 2005. – 342 p. – ISBN13: 978-0-521-45502-2 Atomic physics is one of the oldest fields of physics. A barren and "academic" discipline? Not at all! About ten years ago, atomic physics received a rejuvenating jolt from chaos theory with far reaching implications. Chaos in atomic physics is today one of the most active and prolific areas in...
Cambridge University Press, New York, 2005. — 342 p. — ISBN13: 978-0-521-45502-2. Atomic physics is one of the oldest fields of physics. A barren and "academic" discipline? Not at all! About ten years ago, atomic physics received a rejuvenating jolt from chaos theory with far reaching implications. Chaos in atomic physics is today one of the most active and prolific areas in...
Singapore: World Scientific, 2001. — 323 p. This book provides a comprehensive overview of the topics related to characterization, control and synchronization of complex spatiotemporal phenomena, from both a theoretical and an experimental point of view. It describes applications of these processes in applied mathematics, signal analysis, nonlinear optics, fluid dynamics, chemical...
Academic Press, 2019. — 370 p. — (Emerging Methodologies and Applications in Modelling, Identification and Control). — ISBN: 978-0-12-815838-8. This book is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it...
Springer Cham, 2023. — 374 p. — (Springer Proceedings in Complexity) — eBook ISBN: 978-3-031-37404-3. Specializes on the concepts and methods of dynamical and complex systems Explains the role of mathematics, modeling and numerical simulation Includes lectures on fundamental phenomena, theories and methodologies that arise in complexity This volume of proceedings contains...
Basel: Birkhäuser, 1997. - 400p. A hundred years ago it became known that deterministic systems can exhibit very complex behavior. By proving that ordinary differential equations can exhibit strange behavior, Poincare undermined the founda tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos. Although in the 1930s and 1940s...
Springer, 2001. — 125 p. — (Springer Tracts in Modern Physics) — ISBN: 3540411976 This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems....
New York: Springer, 2021. — 123 p. Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev...
Springer, 2014. — 119 p. — ISBN-13 978-8132220923 Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map...
Singapore: World Scientific, 2009. - 482 p. "Chaos: From Simple Models to Complex Systems" aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools...
New York: Morgan, 2011. — 343 p. This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include...
Springer, 2022. — 100 p. This book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory...
Berlin: Springer, 2006. - 246p.
The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects...
Textbook. — Self-publishing. — Edition 17.6.4: 2023. — XVI, 1093 p. A course on chaos. This book is an advanced textbook on the theory of deterministic, stochastic and quantum chaotic/turbulent systems on level of a 2nd year graduate statistical mechanics or quantum field theory course. Approach it the way that suits you best. A very very short introduction Geometry of chaos...
Boca Raton: CRC Press, 2004. — 256 p. This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations. Orbits of One-Dimensional Systems Bufurcation in...
London: Springer, 1999. — 335 p. Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more...
2nd edition. — New York: Chapman and Hall/CRC, 2020. — 239 p. A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were...
New York: Addison-Wesley, 2000. — 209 p. This book attempts to understand processes in motion such as the movement of stars, the ups and downs of the stock market, the changes in weather, the changes chemicals undergo, and the motion of a pendulum. Students are introduced to chaos, fractals and dynamics, three exciting contemporary mathematics topics, through a combination of...
CRC Press, 2024. — 182 р. — ISBN: 978-1-032-54481-6. The book reviews the application of discrete fractional operators in diverse fields such as biological and chemical reactions, as well as chaotic systems, demonstrating their applications in physics. The dynamical analysis is carried out using equilibrium points of the system for studying their stability properties and the...
Princeton University Press, 2020. — 254 p. Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar...
Springer, 2023. — 328 p. — (UNITEXT for Physics). — ISBN 978-3-031-25153-5. This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems....
Springer, 1999. — 175 p. Foreword - Ilya Prigogine Chaos and Irreversibility Statistical Mechanics of Maps The Bernoulli Map Other One-Dimensional Maps Intrinsic Irreversibility Deterministic Diffusion In appendices: Complex Microstructure of Phase Space More on Mixing Isometry of U_B+ Dual States The Resolvent Formalism Rescaled Legendre Polynomials Formal Expression for the...
New York: Atlantis Press, 2016. - 271 p. The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for...
Springer International Publishing AG, 2017. — 208 p. — ISBN: 9783319478371 From the pioneer works of H. Poincaré to present days, the nonlinear science has developed tremendously. In particular, chaos theory presents nowadays a number of fields of investigation. One of such fields is the so-called routes to chaos, where an interesting one is the chaotic intermittency, because...
2nd Edition. — CRC Press, Taylor & Francis Group, 2007. — 441 p. — ISBN13: 978-1-4200-1104-3. While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on...
Boca Raton: CRC Press, 2013. — 334 p. Comprehensive Review of Hyperbolicity, Ergodicity, and Chaos. Reality of Chaos in the Henon Mapping. Dynamical Properties of the Lozi Mappings. Dynamical Properties of Modified and Generalized Lozi Mappings. Real and Mathematical Applications of Lozi Mappings.
New York: Springer, 2016. — 605 p.
This work represents the third entry of the series of works on “Chaos, Complexity and Leadership”. Contents of the book are composed from broad range of chaos, complexity and their applications in multi disciplines. Articles reflect different perspectives in the field of applied nonlinear methods, modeling of data and simulations as well as...
Springer, 2020. — 291 p. — (Springer Proceedings in Complexity). — ISBN: 978-3-030-27671-3. This book constitutes the proceedings of the 6th International Symposium on Chaos, Complexity and Leadership (ICCLS). Written by interdisciplinary researchers and students from the fields of mathematics, physics, education, economics, political science, statistics, the management...
Springer, 2021. — 317 p. — ISBN 978-3-030-74056-6. This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in...
Springer, 2021. — 317 p. — ISBN 978-3-030-74056-6. This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in...
New York: Springer, 2019. — 715 p. The proceedings of the 2017 Symposium on Chaos, Complexity and Leadership illuminate current research results and academic work from the fields of physics, mathematics, education, economics, as well as management and social sciences. The text explores chaotic and complex systems, as well as chaos and complexity theory in view of their...
Boston: The MIT Press, 1998. — 493 p. In this book, Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is...
Springer 2019. — XIV, 303 p. — ISBN: 978-3-030-32538-1, ISBN: 978-3-030-32537-4. Fills the gap for a concise text at the beginning graduate level; Written by applied mathematicians for applied mathematics students; Takes a holistic approach with deep insights into the subject. This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for applied...
World Scientific Publishing, 2021. — 536 p. — ISBN 978-981-124-345-5. Randomness is an active element relevant to all scientific activities. The book explores the way in which randomness suffuses the human experience, starting with everyday chance events, followed by developments into modern probability theory, statistical mechanics, scientific data analysis, quantum mechanics,...
World Scientific Publishing, 2021. — 536 p. — ISBN 978-981-124-345-5. Randomness is an active element relevant to all scientific activities. The book explores the way in which randomness suffuses the human experience, starting with everyday chance events, followed by developments into modern probability theory, statistical mechanics, scientific data analysis, quantum mechanics,...
Singapore: World Scientific, 1998. — 407 p. This book provides an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc. A unique feature of the book is its systematic application of modern nonlinear and...
New Haven: Yale University Press, 2016. — 526 p. Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet...
New York: Wiley, 2007. - 355p. The only integrative approach to chaos and random fractal theory Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods...
Cambridge, Cambridge University Press, 1998 - 485 стр.
Dynamical system and their linear stability.
Topological chaos.
Liouvillian dynamics.
Probabilistic chaos.
Chaotic scattering.
Scattering theory of transport.
Hydrodynamic models of diffusion.
System maintained out of equilibrium.
Noises as microscopic chaos.
Conclusions and perspectives.
North-Holland, 1991 - 831 стр.
Recent developments in classical mechanics.
Random matrix theories and chaotic dynamics.
The semi-classic quantization of chaotic Hamiltonian systems.
Some quantum-to-classical asymptotics.
Hyperbolic geometry in two dimensions and trace formulas.
Quantum and classical properties of some billiards on the hyperbolic plane.
The classical and...
Wiley-VCH, 2011. — 609 p. A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required...
Wiley, 2002. — 511 p. A new approach to understanding nonlinear dynamics and strange attractors The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the...
Open Road, 2008. — 540 p. A work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time. From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell...
New York: Open Road, 2008. — 475 p. — ISBN: 9781453210482. A work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time. From Edward Lorenz’s discovery of the...
New York: Open Road, 2011. — 370 p. — ISBN: 9781453210475. A work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time. From Edward Lorenz’s discovery of the...
Imperial College Press, 2004. — 223 p. This book presents a comprehensive overview of the research and latest developments in the field of the dynamics of coupled and driven chaotic oscillators, aimed at a wide audience. Since 1990, there has been very active research devoted to the field, culminating in a considerable body of knowledge, while active research continues. The...
Cambridge: Cambridge University Press, 2016. — 418 p. This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete...
Springer, 2011. — 400 p.
It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of...
Singapore: World Scientific Publishing Company, 1998. — 767 p. Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies,...
N.-Y.: Chapman and Hall/CRC, 2012. - 387p.
Now with an extensive introduction to fractal geometry
Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the...
3rd. ed. - Boca Raton: CRC Press, 2024. - 414 p. - (Textbooks in Mathematics). - ISBN 1032677864. Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry . It incorporates i mportant mathematical concepts and backs up the definitions and results with motivation, examples, and applications. The Third Edition...
Boston: The Mathematical Association of America, 2011. - 140p.
With the coming of the computer age, fractals have emerged to play a significant role in art images, scientific application and mathematical analysis. The Beauty of Fractals is in part an exploration of the nature of fractals, including examples which appear in art, and in part a close look at famous classical...
Springer, 1990. — 445 p. Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is...
2nd Edition. — World Scientific Publishing, 2018. — 515 p. — (Peking University–World Scientific Advanced Physics Series, Vol. 4). — ISBN: 978-981-3236-42-4. Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical...
Singapore: World Scientific, 1991. — 530 p. This volume is a collection of more than 7000 full titles of books and papers related to chaotic behaviour in nonlinear dynamics. Emphasis has been made on recent publications, but many publications which appeared before 1980 are also included. Many titles have been checked with the authors. The scope of the Bibliography is not...
World Scientific Publishing, 1989, 460 Pages, ISBN: 9971506823 , 997150698X This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical...
Springer, 1992. — 341 p. Proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, Held at Blydepoort, Eastern Transvaal, South Africa, 13–24 January 1992. Until now the important concept of quantum chaos has remained somewhat ill defined. This volume tackles the ubiquitous borderline between classical andquantum mechanics, studying in particular the...
Addison Wesley, 1994. — 294 s. — ISBN: 978-3-89319-633-3. Die Chaos Theorie und die fraktale Geometrie haben inzwischen ihren Siegeszug um die Welt angetreten. Kaum eine Zeitschrift versäumte es, Ihre Leser mit wunderbaren und kunstvollen Bildern an der Entdeckungsreise in das Reich des Apfelmännchens und der Julia-Mengen teilhaben zu lassen. Das Buch liefert die mathematischen...
An Introduction for Scientist and Engineers.
Oxford University Press, 2004 - 654 p.
This book introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a...
Название: Hirsch M. ,Smale S. , Devaney R. , Differential Equations, Dynamical Systems, and an Introduction to Chaos.
Издательство: Academic.
Год: 2003.
ISBN: 0123497035.
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical...
Taylor & Francis, 2002. - 376 pages.
Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of...
Singapore: World Scientific, 2012. — 428 p. A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the authors' approach to the problem of understanding the compatibility, and even...
Springer, 2000. - 338 pages.
Beginning with ordinary language models or realistic mathematical models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, the majority of...
Springer Science+Business Media, New York, 2004. — 522 p. — ISBN: 1441923306. The development of the theory of chaotic dynamics and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. This volume collects several of the most influential papers in chaos theory from the past 40 years, starting with...
Springer, 2012. — 232 pages. — ISBN: 1461417961
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the...
Germany, Springer, 2007 - 710 стр.
This textbook is an introduction to and exploration of a number of core topics in the field of applied mechanics. On the basis of Lagrange's Principle, a Central Equation of Dynamics is presented which yields a unified view on existing methods. From these, the Projection Equation is selected for the derivation of the motion equations of...
Amsterdam: Springer, 2007. — 711 p. If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this...
An Introduction for Natural Scientists and Engineers. North-Holland, 1994 - 756 стр.
This volume is intended as a detailed introduction to the theory of chaos and is addressed to physicists and engineers who wish to be acquainted with this new and exciting science associated with non-linear deterministic systems. Mathematics are a pre-requisite tool.
Preliminaries.
Mathematical...
World Scientific, 1999. - 768 pages. ISBN10: 9810234341, 9810234333 A compilation of review papers, exposition and technical works of Leo Kadanoff, a theoretical physicist, the aim of this text is to provide not-too-technical writing in which he discusses some issues in condensed matter physics, hydrodynamics, applied mathematics and national policy. The book is divided into...
Springer, 1998. — 140 p. — ISBN13: 978-3-540-63515-4. Chaos occurs widely in both natural and man-made systems. Recently, examples of the potential usefulness of chaotic behavior have caused growing interest among engineers and applied scientists. In this book the new mathematical ideas in nonlinear dynamics are described in such a way that engineers can apply them to real...
John Wiley & Sons, 1999. - 267 pages.
The study of nonlinear dynamics is one of the most active fields in modern science. It reaches across the whole range of scientific study, and is applied in fields as diverse as physics, engineering, biology, economics and medicine. However, the mathematical language used to describe nonlinear dynamics, and the proliferation of new...
New York: Academic Press, 2022. — 352 p. Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical...
Oxford: Oxford University Press, 2010. — 384 p. Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle,...
Chicago: The University of Chicago Press2008. - 288p.
What happens to scientific knowledge when researchers outside the natural sciences bring elements of the latest trend across disciplinary boundaries for their own purposes? Researchers in fields from anthropology to family therapy and traffic planning employ the concepts, methods, and results of chaos theory to harness the...
Springer, 2014. — 346 p. — (CISM International Centre for Mechanical Sciences: Courses and Lectures 555). — ISBN 978-3-7091-1790-3. Модальный анализ нелинейных механических систем This book contains lecture material from CISM course on Modal Analysis of Nonlinear Mechanical Systems, delivered in June 25-29, 2012. The concept of normal modes is central in the theory of linear...
World Scientific Publishing Co. Pte. Ltd., 2016. — 299 p. — ISBN: 1783267968 Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their...
Scribner, 2024. — 336 p. Want to know what chaos theory can teach us about human events? In the perspective-altering tradition of Malcolm Gladwell’s The Tipping Point and Nassim Nicholas Taleb’s The Black Swan comes a provocative challenge to how we think our world works—and why small, chance events can divert our lives and change everything, by social scientist and Atlantic...
Springer-verlag, 2008. 352 р. ISBN 978-3-540-63893-3 (2nd ed. ) This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially...
1st ed. Springer-Verlag Berlin Heidelberg New York, 1994, 1999. 312 p. ISBN:3-540-57457-3. 2nd ed. Springer-Verlag Berlin Heidelberg New York, 1994, 1999. 312 p. ISBN:3-540-63893-8. Overview and Basic Concepts. Nonlinear Dynamics and Deterministic Chaos. Billiard Systems. Gravitational Billiards: The Wedge. The Double Pendulum. Chaotic Scattering. Fermi Acceleration. The...
Springer, 2010. - 249 p. - At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of...
Springer, 2011. - 538 pages.
In a dynamical system, transients are temporal evolutions preceding the asymptotic dynamics. Transient dynamics can be more relevant than the asymptotic states of the system in terms of the observation, modeling, prediction, and control of the system. As a result, transients are important to dynamical systems arising from a wide range of disciplines...
Singapore: World Scientific Publishing Company, 2023. - 216 p. - (Problem Solving In Mathematics And Beyond, 29). - ISBN 9811273243. This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems...
Springer, 1994. — 490 p. The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the...
New York, USA: Cambridge University Press, 2015. — 343 p. — ISBN10: 1107433975. Order and stability are tenuous and fragile. People have to work to create and sustain a semblance of stability and order in their lives and in their organizations and larger communities. Order on the Edge of Chaos compares different ideas about how we coordinate and cooperate. The ideas come from...
Springer (India) Pvt. Ltd. 2015. – 622 p. – ISBN: 978-81-322-2555-3, DOI: 10.1007/978-81-322-2556-0. The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and...
Springer (India) Pvt. Ltd. 2015. – 622 p. – ISBN: 978-81-322-2555-3, DOI: 10.1007/978-81-322-2556-0. The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and...
2nd. ed. — Springer, 2024. — 700 p. — (University Texts in the Mathematical Sciences). — ISBN 9819976944. This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes...
2nd Edition. — Springer, Singapore, 2024. — 701 p. — ISBN 978-981-99-7694-2. This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable...
СПб.: St. Petersburg University Press, 2008. — 161 p. This book might be more accurately titled, “On the advantages of the classical theory of stability of motion in the study of strange attractors.” In almost any solid survey or book on chaotic dynamics, one encounters notions from classical stability theory such as Lyapunov exponent and characteristic exponent. But the effect of...
Oxford University Press, 1998. — 268 p. Fractals and chaos are currently generating excitement across various scientific and medical disciplines. Biomedical investigators, graduate students, and undergraduates are becoming increasingly interested in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This accessible text lucidly...
Springer International Publishing, Switzerland, 2017. — 367 p. — ISBN: 3319449672 This book addresses the linear and nonlinear two-phase stability of the one-dimensional Two-Fluid Model (TFM) material waves and the numerical methods used to solve it. The TFM fluid dynamic stability is a problem that remains open since its inception more than forty years ago. The difficulty is...
Название: Lorenz E. , The Essence of Chaos.
Издательство: University of Washington.
Год: 1996.
ISBN-10: 0295975148.
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of...
CRC, 2005. — 229 p. — ISBN: 0-203-21458-7. Chaos surrounds us. Seemingly random events -- the flapping of a flag, a storm-driven wave striking the shore, a pinball's path -- often appear to have no order, no rational pattern. Explicating the theory of chaos and the consequences of its principal findings -- that actual, precise rules may govern such apparently random behavior --...
New Jersey: World Scientific Publishing, 2021. — 253 p. Welcome to the world of scale symmetry, the last elementary symmetry and the least explored! Find out how this long-neglected element transforms the traditional geometry of lines and planes into a rich landscape of trees, craggy mountains and rolling oceans. Enjoy a visual exploration through the intricate and elaborate...
Hoboken: Wiley, 2014. - 270p. Exact analytical solutions to periodic motions in nonlineardynamical systems are almost not possible. Since the 18th century,one has extensively used techniques such as perturbation methods toobtain approximate analytical solutions of periodic motions innonlinear systems. However, the perturbation methods cannot providethe enough accuracy of...
N.-Y.: Wiley, 2014. - 274p. Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but...
Springer, 2015. — 316 p. — (Nonlinear Physical Science). — ISBN: 978-3-662-47274-3. This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit...
New York: Springer, 2016. — 203 p.
Facilitates discovery of analytical solutions of nonlinear time-delay systems
Illustrates bifurcation trees of periodic motions to chaos
Helps readers identify motion complexity and singularity
Explains procedures for determining stability, bifurcation and chaos
This book for the first time examines periodic motions to chaos in time-delay...
World Scientific Publishing Company, 2004. - 408 pages.
This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and...
Cambridge University Press, 1991. - 377 Pages. Surveying both theoretical and experimental aspects of chaotic behavior, this book presents chaos as a model for many seemingly random processes in nature. Basic notions from the theory of dynamical systems, bifurcation theory and the properties of chaotic solutions are then described and illustrated by examples. A review of...
Wiley, 1999. - 335 p. - The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to...
John Wiley & Sons, 1999. - 334 Pages. ISBN: 0471319759
A timely, accessible introduction to the mathematics of chaos.
The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics,...
New York: Springer, 2015. - 242p. This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular,...
Singapore: World Scientific, 2018. — 251 p. Modern technological, biological, and socioeconomic systems are extremely complex. The study of such systems largely relies on the concepts of competition and cooperation (synchronization). The main approaches to the study of nonlinear dynamics of complex systems are now associated with models of collective dynamics of networks and...
Cambridge University Press, 1993. — 349 p. This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal...
2nd Edition. — Lawrence Erlbaum Associates, Inc., 2005. — 289 p. — ISBN: 0805848738. Putting a New Spin on Groups: The Science of Chaos, Second Edition continues to challenge orthodoxy and static ideas about small group dynamics. A primary goal is to offer an alternative model of group development that addresses three factors: *The model integrates old ideas from previous...
2nd Edition. – Springer Science+Business Media, LLC, 2009. — 404 p. — (Applied Mathematical Sciences 90) — ISBN: 978-0-387-09723-7. This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the...
O’Reilly Media, 2019. — 178 p. — ISBN: 1492051004. Most companies work hard to avoid costly failures, but in complex systems a better approach is to embrace and learn from them. Through chaos engineering, you can proactively hunt for evidence of system weaknesses before they trigger a crisis. This practical book shows software developers and system administrators how to plan...
O’Reilly Media, 2019. — 178 p. — ISBN: 978-1-492-05100-8. Most companies work hard to avoid costly failures, but in complex systems a better approach is to embrace and learn from them. Through chaos engineering, you can proactively hunt for evidence of system weaknesses before they trigger a crisis. This practical book shows software developers and system administrators how to...
O’Reilly Media, 2019. — 178 p. — ISBN: 978-1-492-05100-8. Most companies work hard to avoid costly failures, but in complex systems a better approach is to embrace and learn from them. Through chaos engineering, you can proactively hunt for evidence of system weaknesses before they trigger a crisis. This practical book shows software developers and system administrators how to...
O’Reilly Media, 2019. — 178 p. — ISBN: 978-1-492-05100-8. Most companies work hard to avoid costly failures, but in complex systems a better approach is to embrace and learn from them. Through chaos engineering, you can proactively hunt for evidence of system weaknesses before they trigger a crisis. This practical book shows software developers and system administrators how to...
O’Reilly Media, 2019. — 178 p. — ISBN: 978-1-492-05100-8. Code files only! Most companies work hard to avoid costly failures, but in complex systems a better approach is to embrace and learn from them. Through chaos engineering, you can proactively hunt for evidence of system weaknesses before they trigger a crisis. This practical book shows software developers and system...
Springer, 2021. — 105 p. — (Studies in Systems, Decision and Control 312). — ISBN: 978-3-030-57678-3. This book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus...
Wiley, 2004. — 527 p. — ISBN13: 978- 0-471-54571-2. The purpose of this book is to help translate the new mathematical ideas in nonlinear dynamics into language that engineers and scientists can use and apply to physical systems. Chapter 1 includes an introduction to classical nonlinear dynamics; however, if the book is used as a text, additional supplemental material is...
John Wiley & Sons, Inc., Hoboken, New Jersey, 2004. XIX, 309 p. — ISBN: 0-471-67908-9. Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in...
John Wiley & Sons, Inc., Hoboken, New Jersey, 2004. XIX, 309 p. — ISBN: 0-471-67908-9. Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in...
Arcler Press, 2020. — 488 p. The book "Fractal Analysis" is a collection of contemporaneous articles aims to guide the reader through the world of fractals. A world of computer-generated self-similar patterns that can capture the intricacy of natural structure such as snowflakes, fern leaves, and tree branching. A world that is not only aesthetically pleasing but that is also...
Springer, 1997. - 299 pp. This monograph consists of two parts and gives an approach to the physics of open nonequilibrium systems. Part I derives the phenomena of dissipative structures on the basis of reduced evolution equations and includes Bénard convection and Belousov-Zhabotinskii chemical reactions. Part II discusses the physics and structures of chaos. While presenting...
Singapore: World Scientific Publishing Company, 2002. — 440 p. The cooperative behavior of coupled nonhnear oscillators is of interest in connection with a wide variety of different phenomena in physics, engineering, biology, and economics. Networks of coupled nonlinear oscillators have served as models of spatio-temporal pattern formation and simple forms of turbulence....
Clarendon Press, 1994. — 314 p. This book captures the excitement of the expert contributors working at the forefront of this new area of science, detailing the latest developments in the different fields; from physics to biology, chemistry, the weather, quantum mechanics, and engineering. The nature of chaos is an edited and updated version of a highly popular lecture series...
Springer, 2015. — 234 p. — (Emergence, Complexity and Computation ECC 16). — ISBN: 978-3-319-18104-2. The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation...
Institute of Physics, 1998. — 168 p. — ISBN: 0-7503-0508-8. Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena focuses on explaining the fundamentals of the subject by studying examples from one-dimensional maps and simple differential equations. The book includes numerous line diagrams and computer graphics as well as problems and solutions to test readers'...
Wiley-VCH, 2004. — 700 p. A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to...
Boston: Kluwer Academic, 1992. — 508 p. Mathematical Models of Deterministic Discrete and Continuous Dynamical Systems Order and Chaos as Two General Basic Trends in the Evolution of Dynamical Systems Stochasticity Transformers, Amplifiers and Generators Brief Survey of Studies Related to the Appearance of the Problem of Chaotic and Stochastic Motions and to Turbulence Theory...
Singapore: World Scientific Publishing Co Pte Ltd, 1997. — 314 p. The basic procedures for designing and analysing electronic systems are based largely on the assumptions of linear behavior of the system. Nonlinearities inherent in all real applications very often cause unexpected and even strange behavior. This book presents an electronic engineer's perspective on chaos and...
Nova Science Publishing, 2008. - 360 pages. This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos...
Hauppauge: Nova Science Publishers, Incorporated, 2008. — 482 p. This book presents new international research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronization, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this...
2nd ed. — Cambridge University Press, 2002. — xii+478 p. — ISBN: 978-0-521-81196-5. Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and...
Wiley, 1994. — 425 p. Demonstrates how a basic knowledge of chaos theory can be used to evaluate chaotic experimental time series data and how to apply the presence of chaos to achieve practical goals. After familiarizing the reader with fundamental concepts of chaos, the text introduces the important topics of dimension, symbolic dynamics, Lyapunov exponents and entropy. Contains...
Cambridge University Press, 1993. — 385 p. This book is an in-depth and broad text on the subject of chaos in dynamical systems. It is intended to serve both as a graduate course text for science and engineering students, and as a reference and introduction to the subject for researchers. Within the past decade scientists, mathematicians and engineers have realized that a large...
Singapore: World Scientific, 2023. — 218 p. In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the...
Cambridge: Cambridge University Press, 1993. — 126 p. This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations...
Basic Books, 2022. — 320 p. Learn how the tools that enabled us to overcome the uncertainty of the weather will enable us to find new answers to modern science's most pressing questions. Why does your weather app say “There’s a 10% chance of rain” instead of “It will be sunny tomorrow”? In large part this is due to the insight of Tim Palmer, who made uncertainty essential to...
Manning Publications, 2021. — 325 p. — ISBN 9781617297755. In Chaos Engineering: Crash test your applications , you’ll learn to design and execute controlled failure experiments that reveal the hidden problems in your software. Using a toolbox of open source tools, you’ll inject system-shaking failures at every level. Auto engineers test the safety of a car by intentionally...
Manning Publications, 2021. — 325 p. — ISBN 9781617297755. In Chaos Engineering: Crash test your applications , you’ll learn to design and execute controlled failure experiments that reveal the hidden problems in your software. Using a toolbox of open source tools, you’ll inject system-shaking failures at every level. Auto engineers test the safety of a car by intentionally...
Manning Publications, 2021. — 325 p. — ISBN 9781617297755. In Chaos Engineering: Crash test your applications , you’ll learn to design and execute controlled failure experiments that reveal the hidden problems in your software. Using a toolbox of open source tools, you’ll inject system-shaking failures at every level. Auto engineers test the safety of a car by intentionally...
Manning Publications, 2021. — 426 p. — ISBN 9781617297755. Code Files Only! In Chaos Engineering: Crash test your applications , you’ll learn to design and execute controlled failure experiments that reveal the hidden problems in your software. Using a toolbox of open source tools, you’ll inject system-shaking failures at every level. Auto engineers test the safety of a car by...
Mailand: Springer, 2011. — 290 p. The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic...
2nd Edition. - Springer, 2004. - 894 p. - The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were...
Elsevier, 1998. — 417 p. These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise...
Cambridge: Cambridge University Press, 2017. — 693 p. This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and...
Dover edition, 2007. (McGraw-Hill, Inc., New York, 1981). — 353 p. — (Dover Books on Mathematics). — ISBN: 048645844X. Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest...
Predrag Cvitanovic, Roberto Artuso, Per Dahlqvist, Ronnie Mainieri, Gregor Tanner, Gabor Vattay, Niall Whelan, Andreas Wirzba.
Classical and quantum chaos book.
2002 - 739 стр.
In the world of everyday, moderately turbulent fluids flowing across planes and down pipes, a velvet revolution is taking place. Experiments are as detailed as simulations, there is a zoo of exact...
Bantam Books, 1984. — 349 p. — ISBN: 0553340824. Ilya Prigogine, winner of the Nobel Prize in 1977 for his work on the thermodynamics of non-equilibrium systems, makes his ideas accessible to a wide audience in this book, which has engendered massive debate in Europe and America. He and his colleague, Isabelle Stengers, show how the two great themes of classic science, order...
Springer, 1989. — 297 p. — ISBN: 978-0387970929. 1-systems are a mathematical formalism which was proposed by Aristid 1indenmayer in 1968 as a foundation for an axiomatic theory of develop ment. The notion promptly attracted the attention of computer scientists, who investigated 1-systems from the viewpoint of formal language theory. This theoretical line of research was...
New York, USA: Nova Science, 2016. — 192 p. — (Mathematics Research Developments). This book provides new research on Chaos Theory. Chapter One begins with a discussion on the applications of Chaos Theory to financial statements. Chapter Two describes how the Chaos Theory of Careers developed out of discontent with previous career development theories and how fundamental...
Springer-Verlag, 1992 - 550 стр.
Overview
Part I: Classical systems
Fundamental concepts
Area Preserving Maps
Global Properties
Part II: Quantum systems
Quantum Integrability
Random Matrix Theory
Observed Spectra
Semi-Classical Theory
Driven Systems
Part III: Stochastic Systems
Stochastic Systems
Part IV: Appendices
A. Classical Mechanics
B. Simple Models
C....
USA, Springer-Verlag, 2004 - 693 стр.
Overview
Fundamental concepts
Area Preserving Maps
Global Properties
Random Matrix Theory
Bounded Quantum Systems
Manifestations of Chaos in Quantum Scattering Processes
Semiclassical Theory - Path Integrals
Driven Systems
Time-Periodic Systems
Stochastic Manifestations of Chaos
A. Classical Mechanics
B. Simple Models
C....
Springer, 2020. — 242 p. — (Understanding Complex Systems). — ISBN: 978-3-030-44304-7. Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never...
Princeton University Press, 1991. — 214 p. How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic. "Chance has its reason, "...
Princeton: Princeton University Press, 1991. — 214 p. — ISBN10: 0691021007; ISBN13: 978-0691021003 — (Princeton Science Library. Book 11) How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of...
American Mathematical Society, 2017. — 231 p. — (University Lecture Series 67). — ISBN: 147042956X. The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known,...
World Scientific, 2010. - 440 p. - Series on Stability, Vibration and Control of Systems, Series B, Vol.
16. - This review volume consists an indispensable collection of research papers chronicling the recent progress in controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this...
4th edition. — Icon Books, 2004. — 176 p. — ISBN10: 1848310137, ISBN13: 9781848310131. "Introducing Chaos" explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos...
4th edition. — Icon Books, 2004. — 176 p. — ISBN 10 1848310137, ISBN 13 9781848310131. "Introducing Chaos" explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos...
Cambridge University Press, 2005, 424 pages Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in...
W H Freeman and Company, 1991. - 429 Pages. ISBN: 0716721368
Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chaos, fractals, and other areas of current research and popular interest. Self-similarity is related...
4th, Revised and Enlarged Edition. Wiley-VCH Verlag GmbH & Co. KGaA, 2005. – 299 pages. Experiments and Simple Models Piecewise Linear Maps and Deterministic Chaos Universal Behavior of Quadratic Maps The Intermittency Route to Chaos Strange Attractors in Dissipative Dynamical Systems The Transition from Quasiperiodicity to Chaos Regular and Irregular Motion in Conservative...
Springer, 2006. — 371 p. This carefully edited book presents a focused debate on the mathematics and physics of chaos, nonlinearity and complexity in nature. It explores the role of non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems that draws on the relevant...
Birkhauser, 1991. — 362 p. This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The...
Springer, 2017. — 116 p. — ISBN: 978-3-319-53721-4. This brief provides a general overview of nonlinear systems that exhibit hidden-attractor behavior, a topic of interest in subjects as divers as physics, mechanics, electronics and secure communications. The brief is intended for readers who want to understand the concepts of the hidden attractor and hidden-attractor systems...
Princeton: Princeton University Press, 2009. — 244 p. The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov...
Amsterdam: Springer, 2017. — 408 p. This authoritative book presents a comprehensive account of the essential roles of nonlinear dynamic and chaos theories in understanding, modeling, and forecasting hydrologic systems. This is done through a systematic presentation of: (1) information on the salient characteristics of hydrologic systems and on the existing theories for their...
World Scientific Publishing Co. Pte. Ltd., 2011. – 467 p. – ISBN: 9814350338 The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling,...
CRC Press, 2016. — 932 p. — ISBN: 9781466590434, eISBN 9781466590441. In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with...
Chapman and Hall/CRC, 2008, 364 p. Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models. Using more than 500 graphs and illustrations, the authors show how to design, estimate, and test an array of models.
Requiring little prior...
Springer International Publishing, Switzerland, 2016. – 268 p. – ISBN: 978-3-319-29699-9 Henri Poincaré is considered to be one of the great minds of mathematics, physics, and astronomy. Apart from his rigorous mathematical and analytical style, he was also renowned for his deep insights into science and the philosophy of science. He developed and contributed to many important...
Springer-Verlag, Berlin, Heidelberg, 2016. – 277 p. – ISBN10: 3662484080 Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a...
Oxford University Press, 2007. — 180 pages. — (Very Short Introductions).
Chaos exists in systems all around us. Even the simplest system can be subject to chaos, denying us accurate predictions of its behavior, and sometimes giving rise to astonishing structures of large-scale order. Here, Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He...
Cambridge University Press, 1998. Chaotic dynamics has been hailed as the third great scientific revolution in physics in this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by...
Berlin: Springer, 2006. — 538 p. Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert...
2nd ed. — Springer, 2006. — 552 p. — ISBN: 978-3-540-30882-9. Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook...
USA, Springer, 1982 - 278 стр. Introduction and Simple Properties. Homoclinic Explosions: The First Homoclinic Explosions. Preturbulence, Strange Attractors and Geometric Models. Period Doubling and Stable Orbits. From Strange Attractor to Period Doubling. Symbolic Descriptions of Orbits: The Stable Manifolds of C1 and C2. Large r. Small b. Other Approaches, Other Systems,...
World Scientific Publishing Company, 2010. - 304 pages.
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz and many others, but it goes on to show that there are many other systems that are...
M&T Books, 1993. — 591 p. Step-by-step instructions lead the reader through the creation of a program that produces an endless number of patterns and musical sounds. The package contains over 350 examples of computer art plus an interactive disk and 3-D glasses. The source code is provided in BASIC, C, C++, Visual Basic for Windows, and in QuickBASIC for Macintosh users. There...
Singapore: World Scientific Publishing, 2021. — 357 p. Chaos is the study of the underlying determinism in the seemingly random phenomena that occur all around us. One of the best experimental demonstrations of chaos occurs in electrical circuits when the parameters are chosen carefully. We will show you how to construct such chaotic circuits for use in your own studies and...
Bibliographisches Institut & F.A. Brockhaus AG, Mannheim, 1991. — 210 p. It was Dr. Johnson, the famous wit and philosopher immortalized by his friend Boswell who once said, "Define your terms, gentleman, define your terms. It saves arguments !" This advice is very helpful when we are dealing with subjects such as chaos and quantum chaos. The name chaos has gathered to itself so...
Dordrecht: Springer. – 2006. – 343 p. (NATO Science Series II. Mathematics, Physics and Chemistry - Vol. 227) This textbook is the culmination of the latest NATO Advanced Study Institute (ASI) in the Cortina series on Celestial Mechanics and Dynamical Astronomy entitled Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems. Based on the lectures of...
Addison Wesley Publishing, 1994. - 498 pages.
An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples.
3rd Edition. — Chapman and Hall/CRC, 2024. — 601 p. — ISBN: 978-0-367-02650-9. The goal of this Third Edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Chemistry, and Engineering is the same as previous editions: to provide a good foundation – and a joyful experience – for anyone who’d like to learn about nonlinear dynamics and chaos from an applied...
3rd Edition. — Chapman and Hall/CRC, 2024. — 601 p. — ISBN: 978-0-429-39849-0. The goal of this Third Edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Chemistry, and Engineering is the same as previous editions: to provide a good foundation – and a joyful experience – for anyone who’d like to learn about nonlinear dynamics and chaos from an applied...
3rd Edition. — Chapman and Hall/CRC, 2024. — 601 p. — ISBN: 978-0-429-39849-0. The goal of this Third Edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Chemistry, and Engineering is the same as previous editions: to provide a good foundation – and a joyful experience – for anyone who’d like to learn about nonlinear dynamics and chaos from an applied...
3rd Edition. — Chapman and Hall/CRC, 2024. — 601 p. — ISBN: 978-0-429-39849-0. The goal of this Third Edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Chemistry, and Engineering is the same as previous editions: to provide a good foundation – and a joyful experience – for anyone who’d like to learn about nonlinear dynamics and chaos from an applied...
Cambridge: Cambridge University Press, 1998. — 709 p. Dynamical systems are pervasive in the modelling of naturally occurring phenomena. Most of the models arising in practice cannot be completely solved by analytic techniques; thus, numerical simulations are of fundamental importance in gaining an understanding of dynamical systems. It is therefore crucial lo understand the...
Elsevier, 2006. — 389 p. Volume 1 in Series: Edited Series on Advances in Nonlinear Science and Complexity. The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of...
Singapore: Springer, 2022. — 254 p. This book highlights the solution algorithms and characteristic analysis methods of fractional-order chaotic systems. Fractal dimensions exist broadly in the study of nature and the development of science and technology. Fractional calculus has become a hot research area in nonlinear science. Fractional-order chaotic systems are an important...
World Scientific Publishing, 2003. - 117 p. - During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that...
Wiley, 1989. — 373 p. Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial...
An Introduction Based on Classical Mechanics. — Cambridge University Press, 2006. — 428 p. It has been discovered over the past few decades that even motions in simple systems can have complex and surprising properties. This volume provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior...
Pasadena: California Institute of Technology, 1987. — 268 p. Be it a physical object or a mathematical model, a nonlinear dynamical system can display complicated aperiodic behavior, or "chaos." In many cases, this chaos is associated with motion on a strange attractor in the system's phase space. And the dimension of the strange attractor indicates the effective number of degrees...
Berlin: Springer, 2010. — 302 p. This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most...
2 edition. — Wiley, 2002. — 460 p. Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and...
Wiley, 2002. — 460 p.
Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos.
InTech, 2011. - 310 pages.
This book presents a collection of major developments in chaos systems covering aspects on chaotic behavioral modeling and simulation, control and synchronization of chaos systems, and applications like secure communications. It is a good source to acquire recent knowledge and ideas for future research on chaos systems and to develop experiments...
CRC Press, 2021. — 267 p. — ISBN 978-0367486686. Mathematicians have devised different chaotic systems that are modeled by integer or fractional-order differential equations, and whose mathematical models can generate chaos or hyperchaos. The numerical methods to simulate those integer and fractional-order chaotic systems are quite different and their exactness is responsible...
Springer, 2020. — 223 p. — ISBN-13 9783030312503. Аналогово-цифровая реализация хаотических схем и приложений дробного порядка This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available...
World Scientific, 1993. — 230 p. This volume is the first in the new series Nonlinear Time Series and Chaos. The general aim of the series is to provide a bridge between the two communities by inviting prominent researchers in their respective fields to give a systematic account of their chosen topics, starting at the beginning and ending with the latest state. It is hoped that...
New York: Springer, 2016. — 599 p. This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative...
Reactive Publishing, 2023. — 261 p. Кодирование Choas: раскрытие непредсказуемого: подход к теории хаоса Step into the enthralling realm where unpredictability and order converge. 'Coding Chaos' guides you through the labyrinth of chaos theory, combining the rigor of computer science with the unpredictability of chaotic systems. With Python as your compass, this book is your...
London: Taylor & Francis Group plc, 2004. - 409p.
A hydroinformatics system represents an electronic knowledge encapsulator that models part of the real world and can be used for the simulation and analysis of physical, chemical and biological processes in water systems, in order to achieve a better management of the aquatic environment.
Springer, 2022. — 202 p. — (Nonlinear Systems and Complexity). — ISBN-13 9783030794118. This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers...
New York: Springer, 2018. — 118 p. This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework for composing them. The contributors demonstrate that the associated state networks of digital chaotic systems are strongly connected. They then...
Singapore; World Scientific, 1993. — 247 p. This is the second volume in a series intended to give clear expositions of the applications of the new techniques developed to understand nonlinear phenomena in the life sciences. The first paper by West, Mackey and Chen is methodological in nature and reviews how to distinguish between noise in biomedical data sets and...
Springer, 2003. - 808 pages. This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems....
Bookboon, 2013. — 254 p. — ISBN: 978-87-403-0327-8. This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems. The theory is illuminated by several examples and exercises, many of them taken from population dynamical studies....
Joseph Henry Press, 1997. — 406 p. — ISBN13: 978-0309063517, English. What is this business called 'chaos'? What does it deal with? Why do people think it's important? And how did the term 'chaos' - long associated with disorder - come to signify a new paradigm in the orderly realm of mathematics? The concept of chaos is one of the most exciting and rapidly expanding research...
Joseph Henry Press, 1997. — 406 pages. 1st edition.
ISBN-10: 0309063515 ISBN-13: 978-0309063517
What is this business called 'chaos'? What does it deal with? Why do people think it's important? And how did the term 'chaos' - long associated with disorder - come to signify a new paradigm in the orderly realm of mathematics? The concept of chaos is one of the most exciting and...
ITexLi, 2024. — 131 p. — ISBN 1803564350 9781803564357 1803564342 9781803564340 1803564369 9781803564364. This book contains the method of chaos to detect the level of chaotic motion such as entropy, Lyapunov exponent, Poincare map, and phase-plane diagram. Chaos theory is an interdisciplinary area of scientific study and a branch of engineering focused on the law of dynamic...
Oxford University Press, 2006. — 436 p. The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book...
L.: Imperial College Press, 2007. - 337p.
This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current...
Cambridge University Press, 2009. — 266 p. This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of...
Taylor & Francis Group, LLC, 2012. — 742 pages. ISBN: 1578087228
This book presents a select group of papers that provide a comprehensive view of the models and applications of chaos theory in medicine, biology, ecology, economy, electronics, mechanical, and the human sciences. Covering both the experimental and theoretical aspects of the subject, it examines a range of current...
Singapore: World Scientific Publishing Company, 2011. — 471 p. Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students...
Springer International Publishing AG, 2017. — 149 p. — (New Directions in the Philosophy of Science) — ISBN: 3319546627. The book’s strategy and content will be introduced. Over the last 40 years, chaos theory has had a huge impact on science and philosophy. This is evidenced by the astonishing volume of chaos-related publications; even a cursory survey shows that chaos has...
Саратов: Саратовский государственный университет (СГУ) имени Н.Г. Чернышевского, 2018. — 81 с. В книге систематизируются и развиваются методы аналитического расчета автокорреляционных функций траекторий хаотических отображений различных видов: одномерных кусочно-линейных отображений с полными ветвями (отображающими интервал определения отдельной ветви отображения на полный...
М.: Физматлит, 2007. — 326 с. Рассматриваются динамические системы (каскады) с хаотическим поведением, чьи траекторные, вероятностные и спектральные характеристики которого могут быть представлены аналитически. Предложен метод нахождения собственных чисел и собственных функций оператора Перрона–Фробениуса для кусочно-линейных отображений в пространстве целых функций. Описан...
М.: Физматлит, 2007. — 484 с. В книге дано достаточно полное и аккуратное обсуждение основных подходов к исследованию диссипативных структур, автоволновых процессов и диффузионного хаоса в большом классе различных нелинейных сред. Акцент сделан на классических результатах, полученных в ИПМ им. М.В. Келдыша РАН в научных школах академика А. А. Самарского и чл.-корр. РАН С.П....
М.: Наука. Главная редакция физико-математической литературы, 1992. — 544 с.
Книга посвящена математическому моделированию процессов в открытых нелинейных системах. В качестве примеров рассматриваются математические модели, возникающие в физике плазмы, теории горения, химической кинетике, при математическом моделировании морфогенеза.
Для научных работников, инженеров, студентов...
М.: Наука. Главная редакция физико-математической литературы, 1992. — 544 с. Книга посвящена математическому моделированию процессов в открытых нелинейных системах. В качестве примеров рассматриваются математические модели, возникающие в физике плазмы, теории горения, химической кинетике, при математическом моделировании морфогенеза. Для научных работников, инженеров, студентов...
Пер. с франц. — М.: Мир, 1991. —368 с.
Книга французских авторов представляет собой введение в область исследований, называемую синергетикой. Авторам удалось в живой, непринужденной, вполне доступной форме дать ясное представление о современных познаниях в области физики турбулентности и кооперативных процессов, которыми интенсивно занимаются специалисты по проблемам аэро- и...
Пер. с франц. — М.: Мир, 1991. —368 с.
Книга французских авторов представляет собой введение в область исследований, называемую синергетикой. Авторам удалось в живой, непринужденной, вполне доступной форме дать ясное представление о современных познаниях в области физики турбулентности и кооперативных процессов, которыми интенсивно занимаются специалисты по проблемам аэро- и...
Харьков: Институт монокристаллов, 2005. — 420 с., ил.: 134, библиогр.: 262 назв. — Общ.ред.Б.В.Гринева.
ISBN 966-02-3575-5.
Цель книги — познакомить читателя с новыми направлениями нелинейной физики, сформировавшимися в последнее десятилетие. Выбор материалов для книги авторами ограничивался несколькими соображениями. Прежде всего, в ней рассмотрены существенно нелинейные...
Харьков: Институт монокристаллов, 2005. — 420 с., ил.: 134, библиогр.: 262 назв. — Общ.ред. Б.В.Гринева. - ISBN: 966-02-3575-5. Цель книги — познакомить читателя с новыми направлениями нелинейной физики, сформировавшимися в последнее десятилетие. Выбор материалов для книги авторами ограничивался несколькими соображениями. Прежде всего, в ней рассмотрены существенно нелинейные...
Монография. — Саров: РФЯЦ-ВНИИЭФ, 2016. — 267 с. Монография посвящена динамике систем с цилиндрическим фазовым пространством. Данный класс моделей охватывает механические, квантово-механические, радиотехнические и многие другие системы из различных областей естествознания и технических приложений. Рассматриваются автономные и неавтономные системы с одной, полутора, двумя и...
Учебное пособие. — Воронеж: ВГУ, 2012. — 34 с. Рассмотрено введение в теорию динамических систем с хаотическим поведением. Для студентов физико-математических специальностей университетов. Введение Потоки и каскады Связь с дифференциальными уравнениями. Функция последования (отображение Пуанкаре). Надстройка над диффеоморфизмом Грубые(структурно устойчивые) динамические системы...
Воронеж: ВГУ, 2012. — 34 с. Учебное пособие является введением в теорию динамических систем с хаотическим поведением. Содержание: Введение Потоки и каскады Связь с дифференциальными уравнениями. Функция последования (отображение Пуанкаре). Надстройка над диффеоморфизмом Грубые(структурно устойчивые) динамические системы Подкова Смейла Гиперболический диффеоморфизм Аносова на...
Лекции по нейроинформатике. Брестский государственный технический университет. 2005 - 49 стр.
В лекции рассмотрены нейросетевые методы для обработки хаотических процессов. Изложены стандартные методы для обработки хаотических процессов с целью определения вложенныя динамической системы и идентификации хаоса. Рассмотрен нейросетевой метод для анализа наибольшего показателя...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет им. Н.И. Лобачевского (ННГУ), 2019. — 72 с. Математическая теория динамического хаоса является одним из наиболее интересных и актуальных разделов нелинейной динамики. Благодаря этой теории многие проблемы естествознания и техники получили адекватное описание. Однако, не смотря на весьма...
Киев: наукова думка, 2005. — 282 с. В настоящей книге изложены вводные понятия о явлении динамического хаоса в нелинейных системах. Открытие хаотических режимов в нелинейных системах, моделируемых детерминированными соотношениями, явилось одним из важнейших достижений науки второй половины XX столетия. Приведены начальные сведения о фрактальных структурах, которые можно встретить...
Изд. 3-е, испр. и доп. — М.: Издательство ЛКИ, 2010. — 280 с. , 600 dpi, OCR. В настоящей книге изложены вводные понятия о явлении динамического хаоса в нелинейных системах. Открытие хаотических режимов в нелинейных системах, моделируемых детерминированными соотношениями, явилось одним из важнейших достижений науки второй половины XX столетия. В книге приведены начальные...
Изд. 3-е, испр. и доп. — М.: Издательство ЛКИ, 2010. — 280 с. В настоящей книге изложены вводные понятия о явлении динамического хаоса в нелинейных системах. Открытие хаотических режимов в нелинейных системах, моделируемых детерминированными соотношениями, явилось одним из важнейших достижений науки второй половины XX столетия. В книге приведены начальные сведения о фрактальных...
СПб.: Страта, 2013. — 232 c. — ISBN: 978-5-90615-002-8 Регулярный или динамический хаос был открыт и стал предметом многих статей в глянцевых журналах в последние несколько десятилетий. Это открытие изменяет наши представления о реальности. В новом свете предстают архетипы старых мифов. Хаос - в древнегреческой мифологии - есть предельное распыление материи и одновременно...
СПб.: Страта, 2019. — 218 с. — (Просто). Настоящая книга представляет собой упрощенное изложение основных представлений теории динамического хаоса. Она не предназначена для специалистов в этой области. Эта книга для дилетантов в теории хаоса — для тех, кто живет в самой гуще интенсивного настоящего и вынужден динамично и адекватно реагировать на тенденции и тренды.
Москва; Ижевск: Регулярная и хаотическая динамика, 2004. — 304 c. — ISBN: 5939723233. Эта книга предназначена для тех, кто интересуется основами хаоса. Авторы прослеживают всю историю попыток решить задачи небесной механики, впервые сформулированные в "Началах" Исаака Ньютона. Они знакомят нас с людьми, идеи которых привели к возникновению богатой науки, называющейся нелинейной...
Авторы: Ю.В. Андреев, Ю.В. Гуляев, A. С.Дмитриев, Е.В. Ефремова, Л.В. Кузьмин, B. А. Лазарев, А.И. Рыжов, Т.И. Мохсени — М.: Техносфера, 2019. — 320 с. — ISBN 978-5-94836-541-1. Интригующие свойства динамического хаоса и связанных с ним бифуркационных явлений давно привлекают пристальное внимание исследователей. Достижения в области сложной динамики нелинейных систем позволили...
Авторы: Ю.В. Андреев, Ю.В. Гуляев, A. С.Дмитриев, Е.В. Ефремова, Л.В. Кузьмин, B. А. Лазарев, А.И. Рыжов, Т.И. Мохсени — М.: Техносфера, 2019. — 320 с. — ISBN 978-5-94836-541-1. Интригующие свойства динамического хаоса и связанных с ним бифуркационных явлений давно привлекают пристальное внимание исследователей. Достижения в области сложной динамики нелинейных систем позволили...
М.: Техносфера, 2012. — 436 с. — (Мир физики и техники). — ISBN: 978-5-94836-321-9. Явление динамического хаоса, открытое в последней трети двадцатого века, широко распространено в природе и искусственных системах. Его необычные свойства буквально перевернули обычные представления о том, что малые возмущения или события могут приводить лишь к незначительным изменениям в...
М.: Физматлит, 2002. — 252 с. — ISBN: 5-94052-066-9. Динамический хаос (хаотические колебания) представляет собой нерегулярное и непредсказуемое на большие времена движение в детерминированных нелинейных динамических системах. Причинами нерегулярности и непредсказуемости является собственная динамика системы, а не влияние шумов и внешних возмущающих факторов. Последнее...
М.: Физматлит, 2002. — 252 с. — ISBN: 5-94052-066-9. Динамический хаос (хаотические колебания) представляет собой нерегулярное и непредсказуемое на большие времена движение в детерминированных нелинейных динамических системах. Причинами нерегулярности и непредсказуемости является собственная динамика системы, а не влияние шумов и внешних возмущающих факторов. Последнее...
М.: Наука, 1988. — 368 с. Даётся представление о характерных нелинейных процессах современной классической физики для частиц и полей. Приведены многочисленные примеры. Рассматриваемые явления естественным образом включают как регулярные процессы, так и динамический хаос и турбулентность. Чтение книги не требует от читателя специальной подготовки. Для студентов старших курсов и...
М.: Наука. 1988. — 368 с. Даётся представление о характерных нелинейных процессах современной классической физики для частиц и полей. Приведены многочисленные примеры. Рассматриваемые явления естественным образом включают как регулярные процессы, так и динамический хаос и турбулентность. Чтение книги не требует от читателя специальной подготовки. Для студентов старших курсов и...
Монография. — М.: Наука, 1991. — 235 с. — ISBN 5-02-01471-9. Книга посвящена теории зарождения хаоса в гамильтоновых системах. Изложены основные вопросы теории стохастического слоя и стохастической паутины. Приведены многочисленные примеры из разных областей физики. Рассмотрены приложения методов теории слабого хаоса к проблеме структур сплошной среды (включая проблему...
М.: Физматлит, 2006. — 480 с. Перед Вами издание книги, в основу которой положены три главные концепции классической физики: волны, солитоны, хаос. Помимо недавних результатов, полученных в биологии и теории лазеров, в данное издание авторы включили также новые результаты по преобразованиям солитонов. В конце каждой главы приводятся упражнения и задачи. Книга рассчитана на...
Монография. — Владивосток: Институт биологии моря ДВО РАН, 2004. — 128 с. Монография состоит из двух частей, первая представляет собой адаптированное для биологов и иллюстрированное изложение основных идей нелинейной науки (нередко называемой синергетикой), включающее фрактальную геометрию, теории детерминированного (динамического) хаоса, бифуркаций и катастроф, а также теорию...
Монография. — Владивосток: Институт биологии моря ДВО РАН, 2004. — 128 с. Монография состоит из двух частей, первая представляет собой адаптированное для биологов и иллюстрированное изложение основных идей нелинейной науки (нередко называемой синергетикой), включающее фрактальную геометрию, теории детерминированного (динамического) хаоса, бифуркаций и катастроф, а также теорию...
Учебное пособие. — Ижевск: Удмуртский государственный университет (УдГУ), 2021. — 100 с. — ISBN 978-5-4312-0907-9. В пособии изложены основы теории одномерных и двумерных точечных отображений. На конкретных примерах рассмотрены базовые понятия в динамике линейных и нелинейных систем, в том числе бифуркационный анализ и хаос. Представлены основные аналитические и компьютерные...
Учебное пособие. — М.: Постмаркет, 2000. — 352 с. Первое полноценное учебное пособие по новой, быстроразвивающейся математической дисциплине - до сих пор на русском языке выходили лишь монографии. Хорошо подобранные упражнения и алгоритмы делают книгу отличным пособием для студентов старших курсов и аспирантов, специалистов по приложениям этой теории в различных областях от...
Саратов: ГосУНЦ «Колледж», 2000. - 98с.
В сборнике представлено около 300 задач по нелинейным колебаниям, катастрофам, динамическим системам, бифуркациям, хаосу. Каждый раздел содержит как теоретические задачи, так и задачи исследовательского характера, решаемые с использованием компьютера. Задачи апробированы на Факультете нелинейных процессов Саратовского госуниверситета.
Саратов: ГосУНЦ «Колледж», 2000. - 98с.
В сборнике представлено около 300 задач по нелинейным колебаниям, катастрофам, динамическим системам, бифуркациям, хаосу. Каждый раздел содержит как теоретические задачи, так и задачи исследовательского характера, решаемые с использованием компьютера. Задачи апробированы на Факультете нелинейных процессов Саратовского госуниверситета.
М.: Физматлит, 2001. — 296 с. Излагаются основы представлений о динамическом хаосе - феномене, который активно исследуется в последнее время и встречается в нелинейных системах различной природы - механических, электрических, оптических, химических, биологических. Обсуждаются как простые модельные системы, в которых присутствие хаоса допускает полное обоснование, так и примеры...
Москва ; Ижевск, Институт компьютерных исследований, 2013. — 488 с. Монография посвящена рассмотрению возможности реализации в физических системах структурно устойчивого хаоса, обусловленного присутствием однородно гиперболических аттракторов, таких как соленоид Смейла-Вильямса, DA-аттрактор Смейла, аттракторы типа Плыкина. Дается обзор содержательной части гиперболической...
Перевод статьи: Levi B.G. – Physics Today, April 1986, p.17.
Рассмотрен новый подход, использующий фрактальный формализм при исследовании перехода динамической системы к хаосу. Для сравнения описан переход к хаосу по квазипериодическому сценарию.
УФН,180:12 (2010), 1305-1329.
Обзор знакомит читателей с большинством понятий, используемых при исследовании хаотических явлений, возникающих в нелинейных системах. Его главная цель - дать современое представление о результатах, полученных в теории хаотических динамических систем, и описать оригинальные идеи, лежащие в основе подхода к изучению детерминированного хаоса.
М.: Ленанд, 2011. — 320 с. — ISBN: 978-5-9710-0409-7 В настоящей монографии изложена универсальная бифуркационная теория динамического хаоса во всех нелинейных системах дифференциальных уравнений: диссипативных и консервативных, автономных и неавтономных, обыкновенных, с частными производными и с запаздывающим аргументом, описывающих многочисленные сложные природные,...
М.: Ленанд, 2011. — 320 с. — ISBN: 978-5-9710-0409-7. В настоящей монографии изложена универсальная бифуркационная теория динамического хаоса во всех нелинейных системах дифференциальных уравнений: диссипативных и консервативных, автономных и неавтономных, обыкновенных, с частными производными и с запаздывающим аргументом, описывающих многочисленные сложные природные,...
Учебное пособие. — М.: МАКС Пресс, 2006. — 156 с. Изложены основы новой универсальной теории динамического хаоса в нелинейных диссипативных системах обыкновенных дифференциальных уравнений, в соответствии с которой переход к хаосу во всех таких системах через субгармонические или гомоклинические каскады мягких бифуркаций устойчивых предельных циклов или торов. Пособие...
Учебное пособие. — М.: МАКС Пресс, 2006. — 156 с. В учебном пособии изложены основы новой универсальной ФШМ-теории динамического хаоса в нелинейных диссипативных системах обыкновенных дифференциальных уравнений, в соответствии с которой переход к хаосу во всех таких системах через субгармонические или гомоклинические каскады мягких бифуркаций устойчивых предельных циклов или...
М.: Едиториал УРСС, 2004. — 320 с. В книге представлена во многих случаях отличная от традиционной точка зрения авторов на принципы формирования, сценарии возникновения и способы управления хаотическими режимами поведения в нелинейных диссипативных динамических системах, описываемых обыкновенными дифференциальными уравнениями, уравнениями в частных производных диффузионного...
М.: Едиториал УРСС, 2004. — 320 с. В книге представлена во многих случаях отличная от традиционной точка зрения авторов на принципы формирования, сценарии возникновения и способы управления хаотическими режимами поведения в нелинейных диссипативных динамических системах, описываемых обыкновенными дифференциальными уравнениями, уравнениями в частных производных диффузионного...
Учебное пособие. — М.: Комкнига, 2006. — 280 с. — (Синергетика: от прошлого к будущему). — ISBN 5484001528. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка наметить её...
Учебное пособие. — М.: Комкнига, 2006. — 280 с. — (Синергетика: от прошлого к будущему). — ISBN: 978-5-484-00152-8. В книге рассматриваются некоторые ключевые проблемы современной нелинейной динамики. Концепция авторов сводится к тому, что принципиальные трудности, с которыми столкнулся этот междисциплинарный подход, требуют новой парадигмы. В книге сделана попытка наметить ее...
М. -Ижевск: НИЦ "Регулярная и хаотическая динамика", 2009, 392 с.
Данная книга рассматривает подход к описанию математической и физической Вселенной в целом. Это богато иллюстрированная книга объединяет ранние статьи автора, ставшие сегодня библиографической редкостью, с главами, описывающими историю развития фрактальной геометрии.
Учебное пособие. — СПб.: Санкт-Петербургский государственный технический университет (СПбГТУ), 1998. — 92 с. Материал учебного пособия посвящён теории динамического хаоса. Рассмотрены способы описания стохастических колебаний детерминированных динамических систем. Проведён анализ различных сценариев перехода к хаосу. Представлены наиболее простые с точки зрения изложения...
Монография. — М.: Физматлит, 2012. — 429 с. В монографии рассматривается ряд фундаментальных вопросов, связанных с нелинейной динамикой и хаосом. В частности, даны новые определения инвариантного хаотического множества динамической системы и хаотического аттрактора. Предлагаемые здесь определения позволяют обнаружить новый тип хаотического поведения, реализующийся в...
Учебно-методическое пособие. — Нижний Новгород: Нижегородский государственный университет (ННГУ) имени Н.И. Лобачевского, 2017. — 54 с. При изучении коллективной динамики ансамблей колебательных систем важное значение имеют задачи, связанные с исследованием особенностей их синхронного взаимодействия. В настоящее время известно, что синхронизация элементов со сложной динамикой...
Пер. с англ. — М.: Физматлит, 2007. — 208 с. В книге изложена теория хаотических переходов в динамических системах на плоскости от начальных представлений о хаотическом поведении до обобщенного метода Мельникова - универсального средства анализа хаотического поведения детерминированных и стохастических систем. Приведены примеры решения прикладных задач в области динамики и...
Москва-Ижевск: Институт компьютерных исследований, 2002. – 304 с. Данная книга представляет собой первый шаг в направлении обобщения и классификации самых современных результатов по проблемам компьютерных исследований нелинейных систем. В книге приведены наиболее интересные статьи К. Симо и других авторов, посвященные, как изучению хаоса, его структуры, сценариев развития, так...
Москва-Ижевск: Институт компьютерных исследований, 2002. – 304 с. Данная книга представляет собой первый шаг в направлении обобщения и классификации самых современных результатов по проблемам компьютерных исследований нелинейных систем. В книге приведены наиболее интересные статьи К. Симо и других авторов посвященные, как изучению хаоса, его структуры, сценариев развития, так и...
Basil Blackwell, Cambridge, MA, 1990. – 348 p. - Пер с англ. - М.: 2005. - 386 с. - (Интернет-издание).
Бум публикаций, посвященных хаосу в детерминированных динамических системах, побил все рекорды. Число работ, посвященных этому вопросу и его приложениям, исчисляется десятками тысяч и растет год от года. Вместе с тем отечественные книги на эту тему можно перечислить по пальцам....
Философская литература, 1990. — 348 с. Basil Blackwell, Cambridge,MA. Бум публикаций, посвященных хаосу в детерминированных динамических системах, побил все рекорды. Число работ, посвященных этому вопросу и его приложениям, исчисляется десятками тысяч и растёт год от года. Вместе с тем отечественные книги на эту тему можно перечислить по пальцам. Особенно это касается массовой,...
М.: Едиториал УРСС, 2001. — 320 с. Настоящая монография является одним из классических обзоров по хаосу. Автор проводит читателя от традиционных курсов по дифференциальным уравнениям и классической механике к быстро развивающимся областям нелинейной динамики и хаоса, представляя при этом «старые» и «новые» понятия с единой точки зрения. В книге удачно сочетается одновременное...
Монография. — М.: Едиториал УРСС, 2001. — 320 с. Настоящая монография является одним из классических обзоров по хаосу. Автор проводит читателя от традиционных курсов по дифференциальным уравнениям и классической механике к быстро развивающимся областям нелинейной динамики и хаоса, представляя при этом «старые» и «новые» понятия с единой точки зрения. В книге удачно сочетается...
Монография. — Саратов: Саратовский государственный университет (СГУ) имени Н.Г. Чернышевского, 2021. — 108 с. В монографии исследуются влияние новостного потока на динамику цен и волатильность финансовых рынков, фрактальные свойства потоков новостной интенсивности, а также разрабатываются новые методы и алгоритмы совместного анализа новостных и финансовых данных с применением...
07 с.
Все в мире целиком и полностью имеет свои причины и последствия. Возможно, эта мысль навела меня на осознание того, что все в мире взаимосвязано. Всему есть свои причины. Даже в случайности заложено движение к какой-то цели.
События, кажущиеся случайными, происходят в определенной последовательности.
«Даже в хаосе есть порядок».
Что в точности есть хаос? Название «Теория...
Учебное пособие. — Казань: Казанский федеральный университет (КФУ), 2020. — 36 с. В пособии рассматриваются примеры одномерных и двумерных точечных отображений, исследуются модели динамического хаоса. После изучения студент должен не только расширить свои знания в области нелинейной физики, но и научиться решать поставленные теоретические задачи с использованием вычислительных...
Пер. с англ. А. И. Малышева. — М.: Физматлит, 2004. — 376 с. — ISBN 5-9221-0413-6. Книга является введением в квантовый хаос — квантовую механику систем, хаотических в классическом пределе. Выводы теории всюду иллюстрируются результатами численных расчетов, а также экспериментов с микроволновыми биллиардами, выполненных автором и его группой. После краткого описания опытов с...
М.: Мир, 1988. — 253 с. В книге проф. Г. Шустера (ФРГ) достаточно строго и в то же время доступно изложены основы теории стохастического поведения динамических диссипативных систем. Рассмотрены практически все наиболее важные проблемы в этой области. Кратко изложена хаотическая динамика гамильтоновых систем. Книга написана с большим педагогическим мастерством и хорошо...
Пер. с нем. — М.: Мир, 1988. — 253 с. В книге проф. Г. Шустера (ФРГ) достаточно строго и в то же время доступно изложены основы теории стохастического поведения динамических диссипативных систем. Рассмотрены практически все наиболее важные проблемы в этой области. Кратко изложена хаотическая динамика гамильтоновых систем. Книга написана с большим педагогическим мастерством и...
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