Study Of Several Points Set In Topological Dynamical System

Topological dynamical system is the topological space of a single parameterhomeomorphic transformation group,G.D. Birkhoff other researchers made the study ofthe general theory in early twentieth Century. The scope of its application relate toeconomics, physics, biology and engineering technology. It not only promotes thedevelopment of this discipline of mathematics, but also promotes the development ofsocial science.Return point set, non-wandering point set, ω-limit point set, chain recurrentpoint set are important concepts of topological dynamical system. From the beginningof twentieth Century, many scholars at home and abroad have been made research avariety of properties and relations of point sets, but also have very good results.Withthe development of science, people begin to go a step further to study properties andrelations of point sets in the topological space.On the basis of this study, this article putproperties and relations of the point set in special topological space to research.Researching return point set in a metric space; getting invariance and iterative ofnon-wandering point set in compact metric space; getting invariance and iterative oflimit point set in sequence of compact spaces; getting invariance of chain recurrentpoint set,relation of chain recurrent point set and non-wandering point set in metricspace.The content of the paper is arranged as follows: the first chapter simply introducesdevelopment history and current research status of topological dynamical system, then itintroduces the main contents of this paper; the second chapter systematically introducesrelevant knowledge of topological space and mapping, such as definition of periodicpoint, recurrent point, non-wandering point, ω-limit point, chain recurrent point andthe relevant theorem; the third chapter mainly put return point set, non-wandering point set, ω-limit point set, chain recurrent point set in topological space,metric space,compact metric space, sequence of compact spaces into researching invariance anditerative of point sets and the relationship between the sets of point. Finally, the papersummarizes the main work and conclusions, and move to the next step of the plan.The highlights are: this paper studies properties of recurrent point set, ω-limitpoint set, non-wandering point set, chain recurrent point set in metric space,compactmetric space, sequence of compact spaces, then obtains invariance and iterative of pointsets and relationship between the sets of point.