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Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow

ContributorsMarchese, Luca
Number of pages37
Publication date2010
Abstract

We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in Khinchin' result, then we deduce a sharp estimation on how fast the typical Teichmuller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.

Classification
  • arxiv : math.DS
Citation (ISO format)
MARCHESE, Luca. Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow. 2010, p. 37.
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