Periodic trajectories in 3-dimensional convex billiards |
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Authors: | Michael Farber Serge Tabachnikov |
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Institution: | (1) Department of Mathematics, Tel Aviv University, Ramat Aviv 69978, Israel. e-mail: farber@math.tau.ac.il, IL;(2) Department of Mathematics, Penn State University, University Park, PA 16802, USA. e-mail: tabachni@math.psu.edu, US |
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Abstract: | We give a lower bound on the number of periodic billiard trajectories inside a generic smooth strictly convex closed surface
in 3-space: for odd n, there are at least 2(n-1) such trajectories. Convex plane billiards were studied by G. Birkhoff, and the case of higher dimensional billiards is considered
in our previous papers. We apply a topological approach based on the calculation of cohomology of certain configuration spaces
of points on 2-sphere.
Received: 11 June 2001 / Revised version: 26 February 2002 |
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