Periodic points of the billiard ball map in a convex domain

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28 Scopus citations


We study periodic orbits of the billiard ball map in a strictly convex domain with a C boundary. We conjecture that the Lebesgue measure of all periodic points is 0. We are able to prove the following partial result: the measure of period three periodic orbits is 0. The question of whether the mentioned measure is 0 appeared in the study of spectral invariants of a planar region. The author learned about it from R. Melrose.

Original languageEnglish (US)
Pages (from-to)191-205
Number of pages15
JournalJournal of Differential Geometry
Issue number1
StatePublished - Jul 1989

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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