The Topological Pressure And Multifractal Analysis Of Dynamical System

This article is divided into three parts. In the first part, we will recall the defi-nition of topological pressure, multifractal analysis and amenable group action. In the second part, we use the Cech-Stone compactification to establish a definition of topological pressure on an arbitrary topological space and prove some basic proper-ties of the definition. In the third part, we are devoted to studying the multifractal analysis of the local entropies for arbitrary invariant measures for amenable group actions.The paper is organized as follows:In Chapter 1, the backgrounds of topological entropy, topological pressure,multifractal analysis and amenable group actions are introduced.In Chapter 2, we use the Cech-Stone compactification to establish a definition of topological pressure on an arbitrary topological space. We then prove some basic properties of the definition.In Chapter 3, we give the multifractal analysis of the local entropies for arbitrary invariant measures for amenable group actions.