Lectures on Chaotic Dynamical Systems

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Brand new. We distribute directly for the publisher. 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 explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics.The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis. Read more Show Less

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Overview

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 explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.

Read More Show Less

Product Details

  • ISBN-13: 9780821831687
  • Publisher: American Mathematical Society
  • Publication date: 2/19/2003
  • Series: AMS/IP Studies in Advanced Mathematics Series , #28
  • Edition description: New Edition
  • Pages: 353
  • Product dimensions: 70.00 (w) x 10.00 (h) x 1.00 (d)

Table of Contents

1 Basic Concepts 1
2 Zero-Dimensional Dynamics 51
3 One-Dimensional Dynamics 95
4 Two-Dimensional Dynamics 153
5 Systems with 1.5 Degrees of Freedom 217
6 Generated by 3-D Vector Fields 257
7 Lyapunov Exponents 295
App. 1 Proof of the Annulus Principle 311
App. 2 Normal Form for the Andronov-Hopf-Naimark-Sacker Bifurcation 317
App. 3 Dissipative 'Separatrix Map" 320
App. 4 Derivation of the Zaslavsky map [Z] 322
App. 5 Concluding Remarks on Symbolic Dynamics 325
App. 6 Hyperbolicity Conditions 329
References 339
Index 351
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