Hausdorff dimension of three-period orbits in Birkhoff billiards

Hausdorff dimension of three-period orbits in Birkhoff billiards

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.

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Veröffentlicht in:Nonlinearity 2012-07, Vol.25 (7), p.1947-1954
Hauptverfasser: MERENKOV, Sergei, ZHARNITSKY, Vadim
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical methods in physics
Mathematics
Nonlinearity
Orbits
Other topics in mathematical methods in physics
Physics
Sciences and techniques of general use
Tangents
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/25/7/1947