The Topological Dynamical System For Amenable Group Actions

This thesis studies some contents of topological dynamical systems for amenable group actions. We mainly generalize some concepts, properties and theorems of topological dynamical systems for ? group actions to amenable group actions.This thesis includes the following three parts:In the first part, we firstly introduce the historical background and research progress of topological dynamical system for amenable group actions. Then we introduce the basic concepts for amenable group actions, such as the general definition of dynamical system for amenable group action, recurrence, ? limit set, topological transitivity, topological mixing, almost periodic point and the minimal set and so on.In the second part, by using the method of ergodic theory, we investigate the measure center and the minimal contracting center for amenable group actions. More precisely, we firstly give the definitions of the measure center and the minimal contracting center for amenable group actions, then we get and prove the main result in this chapter: the measure center of a nonempty set equals to its minimal contracting center.In the last part of this thesis, we investigate the new levels of recurrence for amenable group actions: weakly almost periodic point and quasi-weakly almost periodic point. More precisely, we give the definitions of the weakly almost periodic point and the quasi-weakly almost periodic point for amenable group actions and then get some properties of them.