Inhomogeneous Diophantine Approximation and Angular Recurrence for Polygonal Billiards

2001/05/31 by Joerg Schmeling, Serge Troubetzkoy
Mathematics · #math.DS #math.NT #msc:37C #msc:11J

paper · pdf

published as Mat. Sbornik 194 (2003) 295-309. · 13 pages, 1 figure

arxiv created 2001/09/25 · arxiv updated 2009/11/30

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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