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lgli/76/M_Mathematics/MD_Geometry and topology/Tabachnikov S. Geometry and billiards (STML030, AMS, 2005)(ISBN 9780821839195)(600dpi)(T)(O)(192s)_MD_.djvu
Geometry and Billiards (Student Mathematical Library) (Student Mathematical Library, 30) 🔍
Serge Tabachnikov; Pennsylvania State University. Mathematics Advanced Study Semesters American Mathematical Society ; Mathematics Advanced Study Semesters, The Student Mathematical Library, Student Mathematical Library, 2005
English [en] · DJVU · 1.5MB · 2005 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save
description
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 Poincaré 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. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.
Alternative filename
lgrsnf/76/M_Mathematics/MD_Geometry and topology/Tabachnikov S. Geometry and billiards (STML030, AMS, 2005)(ISBN 9780821839195)(600dpi)(T)(O)(192s)_MD_.djvu
Alternative filename
lgli/M_Mathematics/MD_Geometry and topology/Tabachnikov S. Geometry and billiards (STML030, AMS, 2005)(ISBN 9780821839195)(600dpi)(T)(O)(192s)_MD_.djvu
Alternative filename
nexusstc/Geometry and Billiards/58e7bfb67dd4fb42b859b9ba939c7a05.djvu
Alternative author
Serge Tabachnikov; Oleg Aleksandrovich Yakubovskiĭ; American Mathematical Society
Alternative publisher
Education Development Center, Incorporated
Alternative publisher
Jakl
Alternative edition
Student mathematical library, Providence, R.I., [Place of publication not identified, ©2005
Alternative edition
Student mathematical library, No.30, illustrated edition, Providence, Rhode Island, 2005
Alternative edition
Student mathematical library -- v. 30, Providence, R.I, [s.l.], Rhode Island, 2005
Alternative edition
Student mathematical library, v. 30, Providence, Sept. 2005
Alternative edition
American Mathematical Society, [N.p.], 2015
Alternative edition
United States, United States of America
Alternative edition
Student Mathematical Library 030, 2005
Alternative edition
Switzerland, Switzerland
metadata comments
kolxoz -- 76
metadata comments
lg1415822
metadata comments
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metadata comments
Includes bibliographical references (p. 167-173) and index
Alternative description
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 Poincaré 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. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State
Alternative description
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. The 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 (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. A special feature of the book is a substantial number of digressions covering diverse topics related to billiards: evolutes and involutes of plane curves, the $4$-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincaré recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others.
Alternative description
"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."--Jacket.
Alternative description
Chapter 1. Motivation: Mechanics And Optics Chapter 2. Billiard In The Circle And The Square Chapter 3. Billiard Ball Map And Integral Geometry Chapter 4. Billiards Inside Conics And Quadrics Chapter 5. Existence And Non-existence Of Caustics Chapter 6. Periodic Trajectories Chapter 7. Billiards In Polygons Chapter 8. Chaotic Billiards Chapter 9. Dual Billiards Serge Tabachnikov. Includes Bibliographical References (p. 167-173) And Index.
date open sourced
2015-12-12
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