Turbulence Strange Attractors And Chaos
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Turbulence Strange Attractors And Chaos
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Author : David Ruelle
language : en
Publisher: World Scientific
Release Date : 1995
Turbulence Strange Attractors And Chaos written by David Ruelle and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
The present collection of reprints covers the main contributions of David Ruelle, and coauthors, to the theory of chaos and its applications. Several of the papers reproduced here are classics in the field. Others (that were published in less accessible places) may still surprise the reader.The collection contains mathematical articles relevant to chaos, specific articles on the theory, and articles on applications to hydrodynamical turbulence, chemical oscillations, etc.A sound judgement of the value of techniques and applications is crucial in the interdisciplinary field of chaos. For a critical assessment of what has been achieved in this area, the present volume is an invaluable contribution.
Multidimensional Strange Attractors And Turbulence
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Author : I. S. Aranson
language : en
Publisher: CRC Press
Release Date : 1989
Multidimensional Strange Attractors And Turbulence written by I. S. Aranson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
The authors explore the origin of multidimensional strange attractors and their role in describing turbulence. It includes an analytical estimation of the deminsions of strange attractors for models described by differential-difference equations and discusses the conditions in which space-homogeneous chaos is stable with respect to random perturbations in flow systems.
Chaotic Evolution And Strange Attractors
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Author : David Ruelle
language : en
Publisher: Cambridge University Press
Release Date : 1989-09-07
Chaotic Evolution And Strange Attractors written by David Ruelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-07 with Mathematics categories.
This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Strange Attractors
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Author : Michael R. Bütz
language : en
Publisher: John Wiley & Sons
Release Date : 1997
Strange Attractors written by Michael R. Bütz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Family & Relationships categories.
Written by three leaders in the field, Strange Attractors explains how the principles of chaos theory can help mental health professionals arrive at a more profound understanding of the dynamics of one of the most complicated non-linear systems - the family. Both a general introduction to chaos theory and a guide to its clinical applications, Strange Attractors details various chaos-based approaches to the assessment and treatment of families.
The Lorenz Equations
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Author : Colin Sparrow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Lorenz Equations written by Colin Sparrow 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 2012-12-06 with Science categories.
The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.
Chance And Chaos
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Author : David Ruelle
language : en
Publisher: Princeton University Press
Release Date : 2020-06-16
Chance And Chaos written by David Ruelle and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Mathematics categories.
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.
Order Within Chaos
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Author : Pierre Berge
language : en
Publisher: Wiley-VCH
Release Date : 1986
Order Within Chaos written by Pierre Berge and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Presented at a relatively elementary level, this introduction to the study of dissipative dynamical systems is addressed to an audience which is scientifically cultivated but not specialized in this discipline. Encompasses the analysis of all time-dependent phenomena, treating the major types of behavior or of evolution without direct reference to the material aspects. Focuses on physics and chemistry and avoids mathematical treatment. In a panorama which is coherent and accessible, it describes concretely the important dynamical phenomena and the way in which they appear in experimental reality. Covers basic vocabulary and regular periodic behavior, and goes on to apply them in analytical methods.
The Theory Of Chaotic Attractors
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Author : Brian R. Hunt
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-08
The Theory Of Chaotic Attractors written by Brian R. Hunt 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 2004-01-08 with Mathematics categories.
The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.
Nonlinear Dynamics And Chaotic Phenomena An Introduction
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Author : Bhimsen K. Shivamoggi
language : en
Publisher: Springer
Release Date : 2014-05-14
Nonlinear Dynamics And Chaotic Phenomena An Introduction written by Bhimsen K. Shivamoggi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Technology & Engineering categories.
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.
An Exploration Of Dynamical Systems And Chaos
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Author : John H. Argyris
language : en
Publisher: Springer
Release Date : 2015-04-24
An Exploration Of Dynamical Systems And Chaos written by John H. Argyris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Technology & Engineering categories.
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 curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany