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arXiv · 1112.2745

Hausdorff dimension of three-period orbits in Birkhoff billiards

Sergei Merenkov·Vadim Zharnitsky
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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.

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Sergei Merenkov, Vadim Zharnitsky. 2011-12-12. Hausdorff dimension of three-period orbits in Birkhoff billiards. https://doi.org/10.1088/0951-7715%2F25%2F7%2F1947

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