Exponential mixing for the Teichmüller flow in the space of quadratic differentials

Artur Avila; Maria João Resende

doi:10.4171/cmh/263

JournalscmhVol. 87, No. 3pp. 589–638

Exponential mixing for the Teichmüller flow in the space of quadratic differentials

Artur Avila
Université Pierre et Marie Curie, Paris, France
Maria João Resende
Universidade Federal Fluminense, Niterói, Brazil

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Abstract

We consider the Teichmüller 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 Teichmüller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of squares.

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Artur Avila, Maria João Resende, Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Comment. Math. Helv. 87 (2012), no. 3, pp. 589–638

DOI 10.4171/CMH/263