Chaotic Billiards

Nikolai Chernov, Roberto Markarian - Collection Mathematical Surveys and Monographs

316 pages, parution le 31/08/2006

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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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	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