Exponential mixing for the Teichmüller flow

Artur Avila; Sébastien Gouëzel; Jean-Christophe Yoccoz

Publications Mathématiques de l'IHÉS (2006)

  • Volume: 104, page 143-211
  • ISSN: 0073-8301

Abstract

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We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the S L ( 2 , ℝ ) action in the moduli space has a spectral gap.

How to cite

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Avila, Artur, Gouëzel, Sébastien, and Yoccoz, Jean-Christophe. "Exponential mixing for the Teichmüller flow." Publications Mathématiques de l'IHÉS 104 (2006): 143-211. <http://eudml.org/doc/104218>.

@article{Avila2006,
abstract = {We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the $SL(2,\mathbb \{R\})$ action in the moduli space has a spectral gap.},
author = {Avila, Artur, Gouëzel, Sébastien, Yoccoz, Jean-Christophe},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {143-211},
publisher = {Springer},
title = {Exponential mixing for the Teichmüller flow},
url = {http://eudml.org/doc/104218},
volume = {104},
year = {2006},
}

TY - JOUR
AU - Avila, Artur
AU - Gouëzel, Sébastien
AU - Yoccoz, Jean-Christophe
TI - Exponential mixing for the Teichmüller flow
JO - Publications Mathématiques de l'IHÉS
PY - 2006
PB - Springer
VL - 104
SP - 143
EP - 211
AB - We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the $SL(2,\mathbb {R})$ action in the moduli space has a spectral gap.
LA - eng
UR - http://eudml.org/doc/104218
ER -

References

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