Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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)
Authors and Affiliations
Bibliographic Information
Book Title: Exterior Billiards
Book Subtitle: Systems with Impacts Outside Bounded Domains
Authors: Alexander Plakhov
DOI: https://doi.org/10.1007/978-1-4614-4481-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-4480-0Published: 11 September 2012
Softcover ISBN: 978-1-4899-9913-9Published: 15 October 2014
eBook ISBN: 978-1-4614-4481-7Published: 13 September 2012
Edition Number: 1
Number of Pages: XIV, 286
Topics: Dynamical Systems and Ergodic Theory, Calculus of Variations and Optimal Control; Optimization, Mathematical Modeling and Industrial Mathematics