Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
Bulletin de la Société Mathématique de France, Volume 140 (2012) no. 4, pp. 485-532.

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.

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.

DOI: 10.24033/bsmf.2634
Classification: 37D40, 37A20, 11J70, 11K50
Keywords: translation surfaces, Teichmüller flow, Khinchin condition, interval exchange transformations
Mot clés : surfaces de translation, flot de Teichmüller, condition de Khinchin, transformations d'échange d'intervalles
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     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},
     pages = {485--532},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {140},
     number = {4},
     year = {2012},
     doi = {10.24033/bsmf.2634},
     mrnumber = {3059848},
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Marchese, Luca. Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow. Bulletin de la Société Mathématique de France, Volume 140 (2012) no. 4, pp. 485-532. doi : 10.24033/bsmf.2634. http://www.numdam.org/articles/10.24033/bsmf.2634/

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