Winning games for bounded geodesics in Teichmueller discs

Mathematics – Dynamical Systems

Scientific paper

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12 pages, no figures

Scientific paper

We prove that for the flat surface defined by a holomorphic quadratic
differential the set of directions such that the corresponding Teichmueller
geodesic lies in a compact set in the corresponding stratum is a winning set in
Schmidt game. This generalizes a classical result in the case of the torus due
to Schmidt and strengthens a result of Kleinbock and Weiss.

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