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

Cite this article

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