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Chaotic Billiards
 
Nikolai Chernov University of Alabama at Birmingham, Birmingham, AL
Roberto Markarian Universidad de la República, Montevideo, Uruguay
Softcover ISBN:  978-1-4704-7442-3
Product Code:  SURV/127.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-1354-5
Product Code:  SURV/127.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7442-3
eBook: ISBN:  978-1-4704-1354-5
Product Code:  SURV/127.S.B
List Price: $224.00 $161.50
MAA Member Price: $201.60 $145.35
AMS Member Price: $179.20 $129.20
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Chaotic Billiards
Nikolai Chernov University of Alabama at Birmingham, Birmingham, AL
Roberto Markarian Universidad de la República, Montevideo, Uruguay
Softcover ISBN:  978-1-4704-7442-3
Product Code:  SURV/127.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-1354-5
Product Code:  SURV/127.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7442-3
eBook ISBN:  978-1-4704-1354-5
Product Code:  SURV/127.S.B
List Price: $224.00 $161.50
MAA Member Price: $201.60 $145.35
AMS Member Price: $179.20 $129.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1272006; 316 pp
    MSC: Primary 37; Secondary 82;

    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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • 1. Simple examples
    • 2. Basic constructions
    • 3. Lyapunov exponents and hyperbohcity
    • 4. Dispersing billiards
    • 5. Dynamics of unstable manifolds
    • 6. Ergodic properties
    • 7. Statistical properties
    • 8. Bunimovich billiards
    • 9. General focusing chaotic billiards
  • Reviews
     
     
    • Although there are many books covering general mathematical billiards there are no comprehensive introductory texts covering chaotic billiards. The book remedies this deficiency and presents the theory of chaotic billiards in a systematic way.

      Zentralblatt Math
    • In contrast to many other works on billiards, this book does not hide any technicalities. It works out all the technical details, to the last epsilon. There are numerous exercises which are well chosen and useful. This way the reader can not only understand billiard theory in an active way, but can also develop the skills needed to address new questions. Thus it is useful not only graduate students, but also for senior mathematicans who would like to start working on billiards. I strongly recommend this book.

      Mathematical Reviews
  • 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: 1272006; 316 pp
MSC: Primary 37; Secondary 82;

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.

Readership

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

  • Chapters
  • 1. Simple examples
  • 2. Basic constructions
  • 3. Lyapunov exponents and hyperbohcity
  • 4. Dispersing billiards
  • 5. Dynamics of unstable manifolds
  • 6. Ergodic properties
  • 7. Statistical properties
  • 8. Bunimovich billiards
  • 9. General focusing chaotic billiards
  • Although there are many books covering general mathematical billiards there are no comprehensive introductory texts covering chaotic billiards. The book remedies this deficiency and presents the theory of chaotic billiards in a systematic way.

    Zentralblatt Math
  • In contrast to many other works on billiards, this book does not hide any technicalities. It works out all the technical details, to the last epsilon. There are numerous exercises which are well chosen and useful. This way the reader can not only understand billiard theory in an active way, but can also develop the skills needed to address new questions. Thus it is useful not only graduate students, but also for senior mathematicans who would like to start working on billiards. I strongly recommend this book.

    Mathematical Reviews
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.