Periodic trajectories in 3-dimensional convex billiards

被引：0
|
作者：
Michael Farber
Serge Tabachnikov
机构：
[1] Department of Mathematics,
[2] Tel Aviv University,undefined
[3] Ramat Aviv 69978,undefined
[4] Israel. e-mail: farber@math.tau.ac.il,undefined
[5] Department of Mathematics,undefined
[6] Penn State University,undefined
[7] University Park,undefined
[8] PA 16802,undefined
[9] USA. e-mail: tabachni@math.psu.edu,undefined
来源：
manuscripta mathematica | 2002年 / 108卷
关键词：
Configuration Space; Closed Surface; Periodic Trajectory; Topological Approach; Convex Plane;
D O I：
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中图分类号：
学科分类号：
摘要：
 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.
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页码：431 / 437
页数：6
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