The Study Of Two Kinds Of Shadowing Property In Dynamical System

The pseudo-orbit tracing property(POTP) and the average-shadowing property(ASP)were generated along with the study and development of the stability in dynamical system,and had been one of the important properties. In this paper, we mainly study the relationsbetween the POTP and recurrent property, and some properties of the ASP.This thesis consists of three chapters. In the fist chapter, we introduce the background ofshadowing property and some notions.In the second chapter, we study that if the self-mapping of a compact metric space has thePOTP, then the closure of the set of almost period point equals to the set of nonwanderingpoint.In the third chapter, we study the ASP. In section 3.1, it is proved that the hyperboliclinear homeomorphism has the ASP in bounded Banach space. In section 3.2, it is proved thatif a homeomorphism of the compact metric space has the ASP, then it is chain mixing. Insection 3.3, it is proved that if a homeomorphism has the ASP in the compact metric space,and the set of periodic point is dense, then it is Devaney chaos.