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 TreviƱo et Steffen Weil
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[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5079
[4] http://www.mpim-bonn.mpg.de/webfm_send/272/1
[5] http://www.mpim-bonn.mpg.de/webfm_send/272