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Periodic trajectories in 3-dimensional convex billiards

Michael Farber·Serge Tabachnikov
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Abstract

We give 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. We apply a topological approach based on the calculation of cohomology of certain configuration spaces.

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Michael Farber, Serge Tabachnikov. 2001-06-07. Periodic trajectories in 3-dimensional convex billiards. https://arxiv.org/abs/math/0106049

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