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

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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 SL(2,ℝ) 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},
     publisher = {Springer},
     volume = {104},
     year = {2006},
     doi = {10.1007/s10240-006-0001-5},
     mrnumber = {2264836},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-006-0001-5/}
}
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Avila, Artur; Gouëzel, Sébastien; Yoccoz, Jean-Christophe. Exponential mixing for the Teichmüller flow. Publications Mathématiques de l'IHÉS, Tome 104 (2006), pp. 143-211. doi: 10.1007/s10240-006-0001-5

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