Exponential mixing for the Teichmuller flow

Artur Avila (1, 2) , Sébastien Gouëzel (3) , Jean-Christophe Yoccoz (4)

1 IMPA Jean-Christophe Yoccoz
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 CdF (institution) - Collège de France

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.

Mots clés: INTERVAL EXCHANGE TRANSFORMATIONS; ABELIAN DIFFERENTIALS; GEODESIC-FLOW; SPACE; DECAY; SURFACES; THEOREM; MAPS

Domaines: Probabilités [math.PR]

Artur Avila, Sébastien Gouëzel, Jean-Christophe Yoccoz. Exponential mixing for the Teichmuller flow. Publications mathematiques de l' IHES, 2006, 104, pp.143-211. ⟨hal-00364381⟩