2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105075We 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.49 pagesDynamical SystemsGeometric Topologytext