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

Details Khinchin type condition for translation surfaces and asymptotic laws for the Teichmuller flow Khinchin type condition for translation surfaces and asymptotic laws for the Teichmuller flow

2010-03-30

arxiv.org/abs/1003.5887v1

Mathematics

Dynamical Systems

37 pages

Scientific paper

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.

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