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Exponential mixing for the Teichmuller flow

Artur Avila·Sebastien Gouezel·Jean-Christophe Yoccoz
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Abstract

We study the dynamics of the Teichmuller 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 Holder observables. A geometric consequence is that the $\SL(2,\R)$ action in the moduli space has a spectral gap.

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Artur Avila, Sebastien Gouezel, Jean-Christophe Yoccoz. 2005-11-24. Exponential mixing for the Teichmuller flow. https://arxiv.org/abs/math/0511614

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