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Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards

Joerg Schmeling·Serge Troubetzkoy
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Abstract

For a given rotation number we compute the Hausdorff dimension of the set of well approximable numbers. We use this result and an inhomogeneous version of Jarnik's theorem to show strong recurrence properties of the billiard flow in certain polygons

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Joerg Schmeling, Serge Troubetzkoy. 2001-09-25. Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards. https://arxiv.org/abs/math/0105150

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