扩张Thurston映射及相关分支覆盖映射的动力系统和几何性质研究

在本项目中，申请人计划于复动力系统中，借助Sullivan字典的视角，从热动力学机制、遍历论弱扩展性质、素周期轨定理、和乐等分布定理、动力系统相关的随机游走等各个方向对复动力系统中相关分支覆盖映射的动力系统和几何性质进行研究，推广申请人关于扩张Thurston映射的已有工作。

In this project in complex dynamics, from a point of view of Sullivan’s dictionary, the applicant plans to investigate the dynamical and geometric properties of some branched covering maps along the directions of the thermodynamical formalism, weak expansion properties in ergodic theory, prime orbit theorems, holonomy equidistribution theorems, and random walks related to the dynamics, generalizing the applicant’s prior works on expanding Thurston maps.