Propagation of Wawes in Hydrodynamic Flows
Author: Y. A. Stepanyants
Publisher:
Published: 1995
Total Pages: 250
ISBN-13: 9789810223106
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Turbulence, Strange Attractors and Chaos
Author: David Ruelle
Publisher: World Scientific
Published: 1995-09-28
Total Pages: 488
ISBN-13: 9814500240
DOWNLOAD EBOOK →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. Contents:On the Nature of TurbulenceBifurcation in the Presence of a Symmetry GroupThe Ergodic Theory of Axiom A FlowsMicroscopic Fluctuations and TurbulenceStrange AttractorsMeasures Describing a Turbulent FlowDo Turbulent Crystals Exist?Characteristic Exponents for a Viscous Fuid Subjected to Time Dependent ForcesBowen's Formula for the Hausdorff Dimension of Self-Similar SetsErgodic Theory of Chaos and Strange AttractorsLiapunov Exponents from Time SeriesFundamental Limitations for Estimating Dimensions and Lyapunov Exponents in Dynamical SystemsWhere can One Hope to Profitably Apply the Ideas of Chaos? Readership: Nonlinear scientists, researchers in fluid dynamics, mathematical physicists and mathematicians. keywords:Turbulence;Strange Attractor;Chaos;Chemical Oscillation;Ergodic Theory;Turbulent Crystal;Reaction-Diffusion;Hausdorff Dimension;Repeller;Resonance;Recurrence Plot
Turbulence, Strange Attractors, and Chaos
Author: David Ruelle
Publisher: World Scientific
Published: 1995
Total Pages: 496
ISBN-13: 9789810223106
DOWNLOAD EBOOK →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.
Chaotic Evolution and Strange Attractors
Author: David Ruelle
Publisher: Cambridge University Press
Published: 1989-09-07
Total Pages: 114
ISBN-13: 9780521368308
DOWNLOAD EBOOK →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.
Multidimensional Strange Attractors and Turbulence
Author: I. S. Aranson
Publisher: CRC Press
Published: 1989
Total Pages: 94
ISBN-13: 9783718648689
DOWNLOAD EBOOK →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.
The Theory of Chaotic Attractors
Author: Brian R. Hunt
Publisher: Springer Science & Business Media
Published: 2004-01-08
Total Pages: 528
ISBN-13: 9780387403496
DOWNLOAD EBOOK →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.
Strange Attractors
Author: Michael R. Bütz
Publisher: John Wiley & Sons
Published: 1997
Total Pages: 296
ISBN-13:
DOWNLOAD EBOOK →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.
Strange Attractors
Author: Julien C. Sprott
Publisher: M & T Books
Published: 1993
Total Pages: 426
ISBN-13: 9781558512986
DOWNLOAD EBOOK →Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.
An Exploration of Dynamical Systems and Chaos
Author: John H. Argyris
Publisher: Springer
Published: 2015-04-24
Total Pages: 884
ISBN-13: 3662460424
DOWNLOAD EBOOK →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
Nonlinear Dynamics and Chaos
Author: Steven H. Strogatz
Publisher: CRC Press
Published: 2018-05-04
Total Pages: 532
ISBN-13: 0429961111
DOWNLOAD EBOOK →This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
