The Theory of Chaotic Attractors / Edition 1

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Overview

Dedicated to Professor James Yorke, a pioneer in the field of the book includes an extensive, anecdotal introduction discussing Yorke's contributions and giving readers a general overview of the key developments of the theory from a historical perspective.
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Editorial Reviews

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"This book is a collection, from the last 40 years, of the most influential papers in the development of chaos theory. … The editors are eminent in this field … . Their selection of papers is excellent … . it is a book for mathematics graduates specializing in non-linear dynamics. … is a well-presented and well-deserved tribute to the life’s work of Professor Yorke … . might well be as that benchmark that mathematicians of the future will view its publication hundreds of years from now." (Dennis Morris, The Mathematical Gazette, March, 2005)

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Product Details

  • ISBN-13: 9780387403496
  • Publisher: Springer New York
  • Publication date: 1/8/2004
  • Edition description: 2004
  • Edition number: 1
  • Pages: 514
  • Product dimensions: 10.00 (w) x 7.00 (h) x 1.13 (d)

Table of Contents

Preface
Introduction 1
Deterministic Nonperiodic Flow 25
On Invariant Measures for Expanding Differentiable Mappings 37
On the Existence of Invariant Measures for Piecewise Monotonic Transformations 47
The Ergodic Theory of Axiom A Flows 55
Period Three Implies Chaos 77
Simple Mathematical Models with Very Complicated Dynamics 85
A Two-Dimensional Mapping with a Strange Attractor 94
Strange Attractors and Chaotic Motions of Dynamical Systems 103
Ergodic Properties of Invariant Measures for Piecewise Monotonic Transformations 120
The Dimension of Chaotic Attractors 142
Measuring the Strangeness of Strange Attractors 170
Invariant Measures and Variational Principle for Lozi Applications 190
Ergodic Properties of The Lozi Mappings 222
On the Concept of Attractor 243
Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps 265
Ergodic Theory of Chaos and Strange Attractors 273
Another Proof of Jakobson's Theorem and Related Results 313
Unstable Periodic Orbits and the Dimensions of Multifractal Chaotic Attractors 335
Absolutely Continuous Invariant Measures for Piecewise Expanding C[superscript 2] Transformation in R[superscript N] 349
Sinai-Bowen-Ruelle Measures for Certain Henon Maps 364
On the Approximation of Complicated Dynamical Behavior 400
Absolutely Continuous Invariant Measures for Piecewise Real-Analytic Expanding Maps on the Plane 425
SRB Measures for Partially Hyperbolic Systems Whose Central Direction in Mostly Expanding 443
SLYRB Measures: Natural Invariant Measures for Chaotic Systems 491
Credits 513
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