Exponential mixing for the Teichmüller flow
Publications Mathématiques de l'IHÉS, Volume 104 (2006), pp. 143-211.

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 $SL\left(2,ℝ\right)$ action in the moduli space has a spectral gap.

@article{PMIHES_2006__104__143_0,
author = {Avila, Artur and Gou\"ezel, S\'ebastien and Yoccoz, Jean-Christophe},
title = {Exponential mixing for the {Teichm\"uller} flow},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {143--211},
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Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe. Exponential mixing for the Teichmüller flow. Publications Mathématiques de l'IHÉS, Volume 104 (2006), pp. 143-211. doi : 10.1007/s10240-006-0001-5. http://www.numdam.org/articles/10.1007/s10240-006-0001-5/

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