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Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts (Translations of Mathematical Monographs) - Hardcover

Valelrii V. Kozlov And Dmitrii V. Treshchev

 
9780821845509: Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts (Translations of Mathematical Monographs)
Hardcover
ISBN 10: 0821845500 ISBN 13: 9780821845509
Publisher: American Mathematical Society, 1991

Synopsis

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.

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Language Notes

Text: English (translation)
Original Language: Russian

Review

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

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
1991
Language
English
ISBN 10 
0821845500
ISBN 13 
9780821845509
Binding
Hardcover
Number of pages
171