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Bounded geodesics in moduli space

Dmitry Kleinbock·Barak Weiss
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Abstract

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories.The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.

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Dmitry Kleinbock, Barak Weiss. 2003-04-02. Bounded geodesics in moduli space. https://arxiv.org/abs/math/0304029

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