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© 2006

Concepts and Results in Chaotic Dynamics: A Short Course

Textbook

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Pierre Collet, Jean-Pierre Eckmann
    Pages 1-3
  3. Pierre Collet, Jean-Pierre Eckmann
    Pages 5-25
  4. Pierre Collet, Jean-Pierre Eckmann
    Pages 27-43
  5. Pierre Collet, Jean-Pierre Eckmann
    Pages 45-78
  6. Pierre Collet, Jean-Pierre Eckmann
    Pages 79-122
  7. Pierre Collet, Jean-Pierre Eckmann
    Pages 123-140
  8. Pierre Collet, Jean-Pierre Eckmann
    Pages 141-161
  9. Pierre Collet, Jean-Pierre Eckmann
    Pages 163-185
  10. Pierre Collet, Jean-Pierre Eckmann
    Pages 187-214
  11. Back Matter
    Pages 215-232

About this book

Introduction

The study of dynamical systems is a well established field. The authors have written this book in an attempt to provide a panorama of several aspects, that are of interest to mathematicians and physicists alike. The book collects the material of several courses at the graduate level given by the authors. Thus, the exposition avoids detailed proofs in exchange for numerous illustrations and examples, while still maintaining sufficient precision. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.

Keywords

Invariant dynamical systems ergodic theory hyperbolic dynamics proof statistical properties

Authors and affiliations

  1. 1.Center of Theoretical Physics École PolytechniquePalaiseauFrance
  2. 2.Department of Theoretical Physics and Mathematics SectionUniversity of GenevaSwitzerland

Bibliographic information

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Reviews

From the reviews:

"The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. … The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems (at the master’s or Ph.D. level). It is particularly suited for students with interests in applications (either physics, economy or biology)." (Carlangelo Liverani, Mathematical Reviews, Issue 2007 m)

"Two thoughts crossed my mind when I picked up this book. The first was: ‘what a physically attractive book.’ The second was: ‘what a short book to have on such a wide ranging topic.’ … It is a perfect size to carry in a knapsack, the print is clear and the layout of text, equations, and figures is marvelously done. … images are multi-colored stereo images, and allow the reader to ‘see’ a three dimensional effect that helps illustrate the phenomena." (David S. Mazel, MathDL, December, 2007)