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Hardcover ISBN:  9780821845509 
Product Code:  MMONO/89 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445010 
Product Code:  MMONO/89.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845509 
eBook ISBN:  9781470445010 
Product Code:  MMONO/89.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 89; 1991; 171 ppMSC: Primary 34; 58
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.

Table of Contents

Chapters

Introduction: Elements of impact theory

Chapter I. The genetic method in the dynamics of systems with onesided constraints

Chapter II. Periodic trajectories of the Birkhoff billiard

Chapter III. The Hill equation

Chapter IV. Integrable problems

Chapter V. Nonintegrable billiards


Reviews

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


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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.

Chapters

Introduction: Elements of impact theory

Chapter I. The genetic method in the dynamics of systems with onesided constraints

Chapter II. Periodic trajectories of the Birkhoff billiard

Chapter III. The Hill equation

Chapter IV. Integrable problems

Chapter V. Nonintegrable billiards

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