On étude une propriété diophantienne pour les surfaces de translation, définie en termes de connexions de selles et inspirée par la condition de Khinchin classique. On prouve la même dichotomie du théorème de Khinchin et on en déduit une estimation sur la vitesse des excursions à l'infini pour une géodésique de Teichmüller typique dans l'espace des modules des surfaces de translation. Enfin on preuve un résultat plus fort en genre un.
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.
@article{BSMF_2012__140_4_485_0,
author = {Marchese, Luca},
title = {Khinchin type condition for translation surfaces and asymptotic laws for the Teichm\"uller flow},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
volume = {140},
year = {2012},
pages = {485-532},
doi = {10.24033/bsmf.2634},
mrnumber = {3059848},
zbl = {1268.37033},
language = {en},
url = {http://dml.mathdoc.fr/item/BSMF_2012__140_4_485_0}
}
Marchese, Luca. Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow. Bulletin de la Société Mathématique de France, Tome 140 (2012) pp. 485-532. doi : 10.24033/bsmf.2634. http://gdmltest.u-ga.fr/item/BSMF_2012__140_4_485_0/
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