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Chaotic Billiards
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Librairie Eyrolles - Paris 5e
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Résumé

This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena.

The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject.

The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

Sommaire

  • Preface
  • Symbols and Notation
  • Simple Examples
  • Basic Constructions
  • Lyapunov exponents and hyperbolicity
  • Dispersing billiards
  • Dynamics of unstable manifolds
  • Ergodic properties
  • Statistical properties
  • Bunimovich billiards
  • General focusing chaotic billiards
  • Afterword
  • Appendix A: Measure theory
  • Appendix B: Probability theory
  • Appendix C: Ergodic theory
  • Bibliography
  • Index
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Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Nikolai Chernov, Roberto Markarian
Collection Mathematical Surveys and Monographs
Parution 31/08/2006
Nb. de pages 316
Format 18 x 26
Couverture Relié
Poids 732g
Intérieur Noir et Blanc
EAN13 9780821840962
ISBN13 978-0-8218-4096-2

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