Abstract.
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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Received: 11 June 2001 / Revised version: 26 February 2002
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Farber, M., Tabachnikov, S. Periodic trajectories in 3-dimensional convex billiards. Manuscripta Math. 108, 431–437 (2002). https://doi.org/10.1007/s002290200273
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DOI: https://doi.org/10.1007/s002290200273