Hausdorff dimension of three-period orbits in Birkhoff billiards

Sergei Merenkov, Vadim Zharnitsky

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.

Original languageEnglish (US)
Pages (from-to)1947-1954
Number of pages8
JournalNonlinearity
Volume25
Issue number7
DOIs
StatePublished - Jul 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Hausdorff dimension of three-period orbits in Birkhoff billiards'. Together they form a unique fingerprint.

Cite this