Periodic trajectories in 3-dimensional convex billiards

Michael Farber, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)431-437
Number of pages7
JournalManuscripta Mathematica
Volume108
Issue number4
DOIs
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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