Exponential mixing for the Teichmüller flow

• Autores: Artur Avila, Sébastien Gouëzel, Jean-Christophe Yoccoz
• Localización: Publications Mathématiques de L'IHÉS, ISSN 0073-8301, Vol. 104, Nº. 1, 2006, págs. 143-211
• Idioma: inglés
• DOI: 10.1007/s10240-006-0001-5
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• Resumen

  • 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 action in the moduli space has a spectral gap.