**Translations of Mathematical Monographs**

1991;
171 pp;
Hardcover

MSC: Primary 34; 58;
**Print ISBN: 978-0-8218-4550-9
Product Code: MMONO/89**

List Price: $89.00

Individual Member Price: $71.20

# Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts

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*V V Kozlov; D V Treshchev*

Starting with the work of G. D. Birkhoff, billiards have been a
popular research topic drawing on such areas as ergodic theory, Morse theory,
and KAM theory. Billiard systems are also remarkable in that they arise
naturally in a number of important problems of mechanics and physics.

This book is devoted to mathematical aspects of the theory of dynamical
systems of billiard type. Focusing on the genetic approach, the authors
strive to clarify the genesis of the basic ideas and concepts of the theory
of dynamical systems with impact interactions and also to demonstrate that
these methods are natural and effective. Recent limit theorems, which justify
various mathematical models of impact theory, are key features. Questions of
existence and stability of periodic trajectories of elastic billiards occupy
a special place in the book, and considerable attention is devoted to
integrable billiards. A brief survey is given of work on billiards with
ergodic behavior. Each chapter ends with a list of problems.

#### Reviews & Endorsements

Written by well-known mathematicians who have contributed a great deal to the field. The exposition … is very thorough.

-- Mathematical Intellingencer