Relation between hyperbolic structure of partially hyperbolic systems and ergodic limit theorems

点击翻译按钮获取中文摘要

We dealt with discrete time dynamical systems with weak hyperbolic product structure. We established polynomial upper bounds on large deviations for such dynamical systems associated with its Sinai-Ruelle-Bowen(SRB) measure if the return tail of the weak hyperbolic product structure decays polynomially. Applications of our results are some almost Anosov diffeomorphisms with uniformly contracting direction of which restriction on one dimensional center unstable direction behaves as a Manneville-Pomeau map.