Exterior Billiards

Systems with Impacts Outside Bounded Domains

Authors: Plakhov, Alexander

  • ​​​​ 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
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  • ISBN 978-1-4614-4481-7
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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.

Reviews

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)


Table of contents (9 chapters)

  • Notation and Synopsis of Main Results

    Plakhov, Alexander

    Pages 1-20

  • Problem of Minimum Resistance to Translational Motion of Bodies

    Plakhov, Alexander

    Pages 21-54

  • Newton’s Problem in Media with Positive Temperature

    Plakhov, Alexander

    Pages 55-104

  • Scattering in Billiards

    Plakhov, Alexander

    Pages 105-149

  • Problems of Optimal Mass Transportation

    Plakhov, Alexander

    Pages 151-182

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-4481-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4614-4480-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4899-9913-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Exterior Billiards
Book Subtitle
Systems with Impacts Outside Bounded Domains
Authors
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4481-7
DOI
10.1007/978-1-4614-4481-7
Hardcover ISBN
978-1-4614-4480-0
Softcover ISBN
978-1-4899-9913-9
Edition Number
1
Number of Pages
XIV, 286
Topics