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 Geometry and Billiards (Student Mathematical Library)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.
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| Tags: billiards, geometry, billiard, boundary, mathematical, boundary, Mathematical, domain, point, Library |
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Selected Chapters In The Calculus Of Variations
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| Added by: westlife | Karma: 733.12 | Science literature, Maths | 23 May 2009 |
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 These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research. |
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| Tags: variations, calculus, particular, billiards, minimal |
