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 billiard motion, symplectic ...
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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 billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards.The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry.
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Add this copy of Geometry and Billiards to cart. $26.95, good condition, Sold by ThriftBooks-Baltimore rated 4.0 out of 5 stars, ships from Halethorpe, MD, UNITED STATES, published 2005 by American Mathematical Society.
Add this copy of Geometry and Billiards (Student Mathematical Library) to cart. $27.14, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2005 by American Mathematical Society.
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Add this copy of Geometry and Billiards (Student Mathematical Library) to cart. $63.22, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2005 by American Mathematical Society.
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New. Describes billiards and their relation with differential geometry, classical mechanics, and geometrical optics. This book covers such topics as variational principles of billiard motion, and symplectic geometry of rays of light and integral geometry. It is suitable for students interested in ergodic theory and geometry. Series: Student Mathematical Library. Num Pages: 176 pages, Illustrations. BIC Classification: PBM; PBW; WSJZ. Category: (P) Professional & Vocational. Weight in Grams: 242. 2005. Paperback.....We ship daily from our Bookshop.
Add this copy of Geometry and Billiards to cart. $87.85, new condition, Sold by Media Smart rated 3.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 2005 by American Mathematical Society.
Add this copy of Geometry and Billiards (Student Mathematical Library) to cart. $103.89, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2005 by American Mathematical Society.
