Topology of billiard problems, I
Abstract
Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a prescribed final point $B\in X$ and make a prescribed number $n$ of reflections at the boundary $X$. We apply a topological approach based on calculation of cohomology rings of certain configuration spaces.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:math/0006049
 Bibcode:
 2000math......6049F
 Keywords:

 Differential Geometry;
 Algebraic Topology;
 3Dxx;
 58Exx
 EPrint:
 21 pages, 1 figure