Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials

Details Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials

2009-08-07

arxiv.org/abs/0908.1102v1

Mathematics

Dynamical Systems

36 pages, 1 figure

Scientific paper

We consider the Teichmuller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for the restriction of the Teichmuller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of squares.

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