Exponential mixing for the Teichmuller flow
Artur Avila, Sebastien Gouezel, Jean-Christophe Yoccoz
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 (2,) action in the moduli space has a spectral gap.
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