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.

Bibliographische Detailangaben

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
Online-Zugang:	Volltext
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