A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

摘要

Large deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.) 38(3) (2007), 335-376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc. 318(2) (1990), 525-543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata 119 (2006), 121-140].