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

Luca Marchese

Bulletin de la Société Mathématique de France (2012)

  • Volume: 140, Issue: 4, page 485-532
  • ISSN: 0037-9484

Abstract

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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.

How to cite

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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 140.4 (2012): 485-532. <http://eudml.org/doc/272608>.

@article{Marchese2012,
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.},
author = {Marchese, Luca},
journal = {Bulletin de la Société Mathématique de France},
keywords = {translation surfaces; Teichmüller flow; Khinchin condition; interval exchange transformations},
language = {eng},
number = {4},
pages = {485-532},
publisher = {Société mathématique de France},
title = {Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow},
url = {http://eudml.org/doc/272608},
volume = {140},
year = {2012},
}

TY - JOUR
AU - Marchese, Luca
TI - Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
JO - Bulletin de la Société Mathématique de France
PY - 2012
PB - Société mathématique de France
VL - 140
IS - 4
SP - 485
EP - 532
AB - 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.
LA - eng
KW - translation surfaces; Teichmüller flow; Khinchin condition; interval exchange transformations
UR - http://eudml.org/doc/272608
ER -

References

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  11. [11] —, « Logarithmic law for geodesics in moduli space », in Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), Contemp. Math., vol. 150, Amer. Math. Soc., 1993, p. 229–245. Zbl0790.32022MR1234267
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  14. [14] W. A. Veech – « Gauss measures for transformations on the space of interval exchange maps », Ann. of Math.115 (1982), p. 201–242. Zbl0486.28014MR644019
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