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Chaotic Billiards
Nikolai Chernov 
University of Alabama at Birmingham, AL, and Roberto Markarian 
Universidad de la República, Montevideo, Uruguay

Mathematical Surveys and Monographs
2006; 316 pp; hardcover
Volume: 127
ISBN: 0-8218-4096-7
List Price: US$85
Member Price: US$68
Order Code: SURV/127
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Not yet published.
Expected publication date is August 13, 2006.
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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.


Graduate students and research mathematicians interested in mathematical 
physics, statistical mechanics, dynamical systems, and ergodic theory.

Table of Contents

    * 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
    * Measure theory
    * Probability theory
    * Ergodic theory
    * Bibliography
    * Index

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