Topology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards

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dc.creatorFarber, Michael
dc.creatorTabachnikov, Serge
dc.date1999-11-28
dc.date.accessioned2026-07-07T05:31:59Z
dc.date.available2026-07-07T05:31:59Z
dc.descriptionWe give lowed bounds on the number of periodic trajectories in strictly convex smooth billiards in $\R^{m+1}$ for $m\ge 3$. For plane billiards (when m=1) such bounds were obtained by G. Birkhoff in the 1920's. Our proof is based on topological methods of calculus of variations - equivariant Morse and Lusternik - Schirelman theories. We compute the equivariant cohomology ring of the cyclic configuration space of the sphere $S^m$, i.e., the space of n-tuples of points $(x_1, ..., x_n)$, where $x_i\in S^m$ and $x_i\ne x_{i+1}$ for i=1,2, ..., n.
dc.description38 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/9911226
dc.identifierhttp://arxiv.org/abs/math/9911226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79498
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.titleTopology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards
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