Topology of billiard problems, I
Farber, Michael
Duke Math. J., Tome 115 (2002) no. 1, p. 559-585 / Harvested from Project Euclid
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Let $T\subset \mathbf {R}\sp {m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partialT$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed initial 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 the calculation of cohomology rings of certain configuration spaces of $S\sp m$.
Publié le : 2002-12-01
Classification:  55R80,  37C25,  37D50,  37J10,  58E05 
@article{1085598179,
     author = {Farber, Michael},
     title = {Topology of billiard problems, I},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 559-585},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598179}
}

Farber, Michael. Topology of billiard problems, I. Duke Math. J., Tome 115 (2002) no. 1, pp.  559-585. http://gdmltest.u-ga.fr/item/1085598179/