含有真的弱几乎周期点的amenable群作用的动力性状研究

本项目计划针对作用在紧致度量空间上的amenable群作用，引入弱几乎周期点和测度中心等概念，并探索它们的基本性质和相互之间的关系；然后研究含有真的弱几乎周期点的amenable群作用的动力性状，主要包括这样的系统具有何种传递属性和混沌性质，并探索两者之间的联系。含有真的弱几乎周期点的amenable群作用的动力性状一般是很复杂的，对其传递属性和混沌性质加以研究，不仅可以完善拓扑动力系统的基础理论，而且可以为后续的研究提供新的方法或思路。因此本项目计划研究的问题具有重要的理论意义。

This project is planned to introduce the concepts of weakly almost periodic point and measure centre and explore the basic properties as well as the connections of weakly almost periodic point and measure centre for amenable group actions on compact metric spaces and to study the dynamics of such actions with proper weakly almost periodic points. For instance, what transitive properties and chaotic properties such actions should have. Furthermore, the relationships between the transitive properties and the chaotic properties of such actions are also planned to investigate. In general, the dynamics of an amenable group action with proper weakly almost periodic points is very complex, so now to start the studies of transitive properties and chaotic properties of such actions can not only improve the basic theories of topological dynamical systems but can offer some new metholds and ideas for our future reaserches. Thus the problems planned to be studied in the project are of important significance in theory.