Some Dynamical Properties On Hyperspace Of Group Actions

In this thesis,we mainly study the dynamic properties of the hyperspace of group actions,especially the relations on dynamical properties between base space dynamical system and its induced hyperspace dynamical system.The specific arrangements are as follows:The first chapter is the introduction,which gives the research background and research significance of the hyperspace dynamic system.The second chapter is the basic knowledge,which briefly introduces some concepts about hyperspace,group action,free semigroup action and dimension of the metric mean.The third chapter to the fifth chapter is the main content of this paper,which introduces the main research results of this paper in detail.The third chapter focuses on the relationship between the base space dynamical system and its induced hyperspace dynamical system with respect to pointwise periodicity,equicontinuous and pointwise minimal and so on.It is also proved that the topological entropy of hyperspace dynamical system of group action is zero when it is pointwise recurrent.The fifth chapter calculates the numerical relationship between the metric mean dimension of the base space dynamical system and the metric mean dimension of the induced hyperspace dynamical system.The sixth chapter summarizes the main content of this paper and the prospect of future research issues.