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"This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics." "The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisites include only the standard material usually covered in the first two years of college (the entire calculus sequence, linear algebra), readers should show some mathematical maturity and strongly rely on their mathematical common sense. As a reward, they will be taken to the forefront of current research."--BOOK JACKET.

Geometry --- Calculus of variations --- Billiards --- Research --- Research.

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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.

Billiards --- Functions of complex variables. --- Geometry, Differential. --- Differential geometry --- Complex variables --- Cue sports --- Cuesports --- Mathematical models. --- Mathematics. --- Dynamics. --- Ergodic theory. --- Calculus of variations. --- Dynamical Systems and Ergodic Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Elliptic functions --- Functions of real variables --- Ball games --- Differentiable dynamical systems. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Models, Mathematical --- Isoperimetrical problems --- Variations, Calculus of