Notation and Synopsis of Main Results -- Problem of Minimum Resistance to Translational Motion of Bodies -- Newton's Problem in Media with Positive Temperature -- Scattering in Billiards -- Problems of Optimal Mass Transportation -- Problems on Optimization of Mean Resistance -- The Magnus Effect and the Dynamics of a Rough Disc -- Invisible Bodies -- Retroreflectors
Summary
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
Analysis
Mathematics
Differentiable dynamical systems
Mathematical optimization
Dynamical Systems and Ergodic Theory
Calculus of Variations and Optimal Control; Optimization
