© 2013

Exterior Billiards

Systems with Impacts Outside Bounded Domains

  • Examines properties of billiard dynamics outside bounded domains

  • Includes topics such as scattering, resistance, invisibility and retro-reflection?

  • Useful for mathematicians working in dynamical systems


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alexander Plakhov
    Pages 1-20
  3. Alexander Plakhov
    Pages 105-149
  4. Alexander Plakhov
    Pages 151-182
  5. Alexander Plakhov
    Pages 183-195
  6. Alexander Plakhov
    Pages 197-218
  7. Alexander Plakhov
    Pages 219-242
  8. Alexander Plakhov
    Pages 243-277
  9. Back Matter
    Pages 279-284

About this book


A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections from the boundary of a domain. Exterior Billiards presents billiards in the complement of  domains and their applications in aerodynamics and geometrical optics.

 This book distinguishes itself from existing literature by presenting billiard dynamics outside bounded domains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance  and Newton’s problem in media with positive temperature. In chapters 4 and 5, scattering of billiards by nonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamics are addressed next and problems of invisibility and retro-reflection within  the framework of geometric optics conclude the text.

 The book will appeal to mathematicians working in dynamical systems and calculus of variations.  Specialists working in the areas of applications discussed will also find it useful.


Bodies of Maximal and Minimal Resistance Newton's Aerodynamic Problem Optimal Mass Transportation Outside Billiard Scattering by obstacles Shape Optimization

Authors and affiliations

  1. 1., Dept. of MathematicsUniversity of AveiroAveiroPortugal

Bibliographic information


From the reviews:

“The book under review is a very nice presentation of several problems related to the aerodynamics of bodies in highly rarefied media. … The book is very pleasant to read; the various mathematical models are clearly presented, and even a nonspecialist in the field can follow the presentation of the problems. Several pictures that are included greatly help the reader … .” (Giuseppe Buttazzo, SIAM Review, Vol. 56 (1), March, 2014)