Continuous Mapping Measure Pressure And Topology R R Pressure

In this thesis, We introduce the concepts of measure-theoretic r-pressure and topological r-pressure of a continuous map on a compact metric space, and discusses some important properties. Meanwhile, we get the results as follows:Measure-theoretic pressure is the limit of measure-theoretic r-pressure and topological pres-sure is the limit of topological r-pressure (r→0). The paper is organized as follows:In chapter one, we mainly review the development of the entropy and the topo-logical pressure.In chapter two, we recall some classical definitions and lemmas in topological dynamical system and ergodic theory.In chapter three, we introduce the notions of measure-theoretic r-pressure and topological r-pressure, discuss some properties and prove both convergence theorems.