Topological R-Pressure And Topological Pressure Of Free Semigroup Actions

In this dissertation,we mainly study the topological r-pressure and topological pressure of free semigroup actions on compact metric spaces.The main contents can be divided into the following two parts:In the first part,we define the topological r-pressure of free semigroup actions in terms of spanning set and separated set on compact metric space,and obtain the related properties of topological r-pressure of free semigroup actions.Finally,we give the first major result of this dissertation:the relation between topological r-pressure and topological pressure of free semigroup actions,that is,the topological pressure of free semigroup actions is the limit of topological r-pressure as r approaches 0.The second part mainly explains the second result of this dissertation:let fi,i=0,1,…m-1 be homeomorphism on compact metric space,we can use the skew-product transformation as the bridge and get that the topological pressure of f0,…,fm-1 equals the topological pressure of f0-1,…,fm-1-1.