群作用的研究是近年来国际上研究的热点问题。本项目主要研究amenable群作用的遍历性质，包括最大熵测度的存在唯一性以及周期轨道的指数增长率问题，进一步研究非amenable群特别是sofic群作用的相关性质。研究目标是证明满足specification性质的可扩群作用的最大熵测度存在而唯一，以及周期轨道的指数增长率等于系统的拓扑熵。

The study of group actions is one of hot topics in the research of dynamical systems. The project mainly focus on some ergodic properties for amenable group actions including the maximal entropy measures and the growth number of periodic orbits. We will use the structure of amenable groups and the quasi-tiling tools. We want to study the existence and uniqueness of maximal entropy measure and the relationship between the growth of periodic orbits and the topological entropy for expansive systems with specification.