Exponential mixing for the Teichmüller flow

  • Artur AvilaEmail author
  • Sébastien GouëzelEmail author
  • Jean-Christophe YoccozEmail author


We study the dynamics of the Teichmüller 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 Hölder observables. A geometric consequence is that the \(SL(2,\mathbb{R})\) action in the moduli space has a spectral gap.


Modulus Space Translation Surface Saddle Connection John Domain Interval Exchange Transformation 
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© IHES and Springer-Verlag 2006

Authors and Affiliations

  1. 1.CNRS UMR 7599, Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.CNRS UMR 6625, IRMARUniversité de Rennes 1Rennes CedexFrance
  3. 3.Collège de FranceParisFrance

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