Hausdorff dimension of three-period orbits in Birkhoff billiards

Details Hausdorff dimension of three-period orbits in Birkhoff billiards Hausdorff dimension of three-period orbits in Birkhoff billiards

2011-12-12

arxiv.org/abs/1112.2745v1

Mathematics

Dynamical Systems

10 pages, 1 figure

Scientific paper

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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