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Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts
 
Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts
Hardcover ISBN:  978-0-8218-4550-9
Product Code:  MMONO/89
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4501-0
Product Code:  MMONO/89.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4550-9
eBook: ISBN:  978-1-4704-4501-0
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
Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts
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Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts
Hardcover ISBN:  978-0-8218-4550-9
Product Code:  MMONO/89
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4501-0
Product Code:  MMONO/89.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4550-9
eBook ISBN:  978-1-4704-4501-0
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 Details
     
     
    Translations of Mathematical Monographs
    Volume: 891991; 171 pp
    MSC: 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 one-sided 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 well-known mathematicians who have contributed a great deal to the field. The exposition ... is very thorough.

      Mathematical Intellingencer
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 891991; 171 pp
MSC: 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.

  • Chapters
  • Introduction: Elements of impact theory
  • Chapter I. The genetic method in the dynamics of systems with one-sided constraints
  • Chapter II. Periodic trajectories of the Birkhoff billiard
  • Chapter III. The Hill equation
  • Chapter IV. Integrable problems
  • Chapter V. Nonintegrable billiards
  • Written by well-known mathematicians who have contributed a great deal to the field. The exposition ... is very thorough.

    Mathematical Intellingencer
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.