We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition.We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
Marchese L. (2012). Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow. BULLETIN DE LA SOCIÉTÉ MATHÉMATIQUE DE FRANCE, 140(4), 485-532.
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
Marchese L.
2012
Abstract
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition.We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.File in questo prodotto:
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