TY  - BOOK
AU  - Plakhov,Alexander
ED  - SpringerLink (Online service)
TI  - Exterior Billiards: Systems with Impacts Outside Bounded Domains 
SN  - 9781461444817
AV  - QA313 
U1  - 515.39 23
PY  - 2013///
CY  - New York, NY
PB  - Springer New York, Imprint: Springer
KW  - Mathematics
KW  - Dynamics
KW  - Ergodic theory
KW  - Mathematical models
KW  - Calculus of variations
KW  - Dynamical Systems and Ergodic Theory
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Mathematical Modeling and Industrial Mathematics
N2  - 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
UR  - http://dx.doi.org/10.1007/978-1-4614-4481-7
ER  -