Exponential mixing for the Teichmuller flow

Details Exponential mixing for the Teichmuller flow Exponential mixing for the Teichmuller flow

2005-11-24

arxiv.org/abs/math/0511614v1

Mathematics

Dynamical Systems

49 pages

Scientific paper

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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