Chaotic Billiards

Chaotic Billiards

by Nikolai Chernov, Roberto Markarian
     
 

ISBN-10: 0821840967

ISBN-13: 9780821840962

Pub. Date: 08/30/2006

Publisher: American Mathematical Society

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

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Overview

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.

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Product Details

ISBN-13:
9780821840962
Publisher:
American Mathematical Society
Publication date:
08/30/2006
Series:
Mathematical Surveys and Monographs, #127
Pages:
316
Product dimensions:
7.30(w) x 10.30(h) x 0.90(d)

Table of Contents

Ch. 1Simple examples1
Ch. 2Basic constructions19
Ch. 3Lyapunov exponents and hyperbolicity41
Ch. 4Dispersing billiards67
Ch. 5Dynamics of unstable manifolds103
Ch. 6Ergodic properties141
Ch. 7Statistical properties163
Ch. 8Bunimovich billiards207
Ch. 9General focusing chaotic billiards251
App. AMeasure theory
App. BProbability theory
App. CErgodic theory

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