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

研究了具有弱双曲积结构的离散时间动力系统。当弱双曲积结构的返回尾呈多项式衰减时，我们建立了这类动力系统与其sinais - ruelle - bowen （SRB）测度相关的大偏差多项式上界。我们的结果应用于一些方向一致收缩的几乎Anosov微分同态，其在一维中心不稳定方向上的限制表现为一个曼纳维-波默映射。

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.