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1 December 2002 Topology of billiard problems, I
Michael Farber
Duke Math. J. 115(3): 559-585 (1 December 2002). DOI: 10.1215/S0012-7094-02-11535-X

Abstract

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 $S\sp m$.

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Michael Farber. "Topology of billiard problems, I." Duke Math. J. 115 (3) 559 - 585, 1 December 2002. https://doi.org/10.1215/S0012-7094-02-11535-X

Information

Published: 1 December 2002
First available in Project Euclid: 26 May 2004

zbMATH: 1013.37033
MathSciNet: MR1940412
Digital Object Identifier: 10.1215/S0012-7094-02-11535-X

Subjects:
Primary: 55R80
Secondary: 37C25 , 37D50 , 37J10 , 58E05

Rights: Copyright © 2002 Duke University Press

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Vol.115 • No. 3 • 1 December 2002
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