A Survey Of Nonlinear Dynamics Chaos Theory
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A Survey Of Nonlinear Dynamics
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Author : Richard Lee Ingraham
language : en
Publisher: World Scientific
Release Date : 1992
A Survey Of Nonlinear Dynamics written by Richard Lee Ingraham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
This book is intended to give a survey of the whole field of nonlinear dynamics (or ?chaos theory?) in compressed form. It covers quite a range of topics besides the standard ones, for example, pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. The many meanings or measures of ?chaos? in the literature are summarized. A precise definition of chaos based on a carefully limited sensitive dependence is offered. An application to quantum chaos is made. The treatment does not emphasize mathematical rigor but insists that the crucial concepts and theorems be mathematically well-defined. Thus topology plays a basic role. This alone makes this book unique among short surveys, where the inquisitive reader must usually be satisfied with colorful similes, analogies, and hand-waving arguments.Richard Ingraham graduated with B.S. summa cum laude in mathematics from Harvard college and with M.A. and Ph.D in Physics from Harvard Graduate School. He was granted the Sheldon Prize Traveling Fellowship by Harvard College and was a member of the Institute for Advanced Study at Princeton for two years.
A Survey Of Nonlinear Dynamics
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Author : Richard Lee Ingraham
language : en
Publisher:
Release Date : 1991
A Survey Of Nonlinear Dynamics written by Richard Lee Ingraham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Chaotic behavior in systems categories.
Chaos And Nonlinear Dynamics
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Author : Robert C. Hilborn
language : en
Publisher:
Release Date : 2000
Chaos And Nonlinear Dynamics written by Robert C. Hilborn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.
Chaos Concepts Control And Constructive Use
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Author : Yurii Bolotin
language : en
Publisher: Springer
Release Date : 2016-10-24
Chaos Concepts Control And Constructive Use written by Yurii Bolotin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-24 with Science categories.
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Frontiers In The Study Of Chaotic Dynamical Systems With Open Problems
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Author : Elhadj Zeraoulia
language : en
Publisher: World Scientific
Release Date : 2011
Frontiers In The Study Of Chaotic Dynamical Systems With Open Problems written by Elhadj Zeraoulia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.
Nonlinear Dynamical Systems And Chaos
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Author : H.W. Broer
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Nonlinear Dynamical Systems And Chaos written by H.W. Broer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.
A Survey Of Nonlinear Dynamics Chaos Theory
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Author : R L Ingraham
language : en
Publisher: World Scientific
Release Date : 1991-12-11
A Survey Of Nonlinear Dynamics Chaos Theory written by R L Ingraham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-12-11 with Science categories.
This book is intended to give a survey of the whole field of nonlinear dynamics (or “chaos theory”) in compressed form. It covers quite a range of topics besides the standard ones, for example, pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. The many meanings or measures of “chaos” in the literature are summarized. A precise definition of chaos based on a carefully limited sensitive dependence is offered. An application to quantum chaos is made. The treatment does not emphasize mathematical rigor but insists that the crucial concepts and theorems be mathematically well-defined. Thus topology plays a basic role. This alone makes this book unique among short surveys, where the inquisitive reader must usually be satisfied with colorful similes, analogies, and hand-waving arguments. Richard Ingraham graduated with B.S. summa cum laude in mathematics from Harvard college and with M.A. and Ph.D in Physics from Harvard Graduate School. He was granted the Sheldon Prize Traveling Fellowship by Harvard College and was a member of the Institute for Advanced Study at Princeton for two years. Contents:Introductory RemarksFundamentals of Continuous Time SystemsDiscrete Time Systems: Iteration of MapsHamiltonian SystemsMeasures of ChaosRenormalization GroupPartial Differential EquationsExperimental Realizations of Nonlinear Dynamics Readership: Theoretical physicists, applied mathematicians, engineers and biologists in chaos research. keywords:Chaos Theory;Sensitive Dependence on Initial Conditions;Linear vs.Nonlinear;Continuous and Discrete Time Systems;Measures of Chaos;Renormalization Group;Chaos in Quantum Mechanics;Exact Definitions“This book gives a survey of the whole field of nonlinear dynamics (or “chaos theory”) in compressed form. The author states the key definitions and theorems carefully. The book is very short, but its content is comprehensive. This book makes it possible for the reader to understand the main ideas in nonlinear dynamics and to proceed to further research along the lines of the cited literature.”Si Ming Zhu Mathematical Reviews
Chaotic Dynamics Of Nonlinear Systems
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Author : S. Neil Rasband
language : en
Publisher: Wiley-VCH
Release Date : 1997-02-28
Chaotic Dynamics Of Nonlinear Systems written by S. Neil Rasband and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-28 with Science categories.
An introduction to the study of chaotic systems via numerical analysis, this work includes many applications in physics and employs differential equations, linear vector spaces and some Hamiltonian systems. Includes problems.
Nonlinear Dynamics And Chaotic Phenomena
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Author : B.K Shivamoggi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Nonlinear Dynamics And Chaotic Phenomena written by B.K Shivamoggi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.
The Physics Of Phase Space
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Author : Young S. Kim
language : en
Publisher: Springer
Release Date : 2005-09-13
The Physics Of Phase Space written by Young S. Kim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-13 with Science categories.
The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.