Some Research Into Pseudo-orbit Shadowing And Weak Shadowing Property

In this paper, we study some properties of the pseudo-orbit tracing property and the weak shadowing property, and mainly discuss the relationship among totally transitive,chaos,topological double ergodicity and scatterings under the condition that maps of dynamical systems have the POTP or WSP. More precisely,In preface, we briefly introduce the content, methods, development and present conditions in topological dynamical system and the basic structure of this paper.In chapter 1, some preliminary knowledge in topological dynamical system and ergodic theory which will be used in this paper are reviewed.In chapter 2, we study the condition of equicontinuous maps preserving POTP on invariant sets and the relationship among dynamical properties such as totally transitive,topology ergodicity,chaos,scatterings under the condition that maps of dynamical systems have the POTP.In chapter 3, some basic properties of the 2WSP are given firstly. Secondly, we study the 2WSP for inverse limit systems and the relationship between the 2WSP for continuous map on a compact matric space and that for the lift map on a covering space. Finally, we discuss the relationship between the 1WSP and some chaotic properties such as weakly topological mixing, and the relationship among dynamical properties such as totally transitive,topology ergodicity,chaos,scatterings under the condition that maps of dynamical systems have the 1WSP.