Artur Avila, Sebastien Gouezel, Jean-Christophe Yoccoz
Published 2005-11-24Version 1
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.
Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials
Moduli Spaces of Abelian Differentials: The Principal Boundary, Counting Problems and the Siegel--Veech Constants
Invariant and stationary measures for the SL(2,R) action on Moduli space
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