The Rate Of Convergence For Central Limit Theorem In The Kolmogorov Distance For Deterministic Dynamical Systems

This article mainly studies the rate of convergence in the central limit theo-rem for deterministic dynamical systems.We prove the central limit theorem for v_n=??_J=0^n-1v°T^j whereis a H(?)lder continuous observable with a mean of 0 andis a nonuniformly expanding map.After that,we also obtain the convergence rate of v_n in the Kolmogorov distance.In addition to nonuniformly expanding systems,our results are also applicable to nonuniformly hyperbolic systems.