Modefarve Geometry and Billiards by Serge Tabachnikov M1KsPHnN

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Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or equivalently the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry classical mechanics and geometrical optics. Topics covered include variational principles of bi