On the Hausdorff measure of diophantine conditions for a translation surface

For a given translation surface, we prove a version of Khinchin-Jarnick Theorem, which gives a dichotomy on the Hausdorff measure of the set of directions admitting infinitely many diophantine approximations, or in other terms the set of directions generating a Teichmuller geodesics whose maximal excursions at infinity occur at a prescribed speed. Joint work with Rodrigo Treviño et Steffen Weil

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