Study Invariance Of Several Points Set In Dynamical System

In the meaningful process of change and other corresponding physical progress,the corresponding state of the elements in invariant subset is steady. Thus, the invariant subset of mapping is vital to the study of dynamic system.Periodic point set, eventually periodic point set, almost periodic point set and asymptotic periodic point set are important concepts of topological dynamical system.This paper proves the invariance and the inclusive relations of these point sets in one-dimensional self-mapping. And by using the descendible mapping, it extends invariance to n-dimensional self-mapping and broadens the scope of research. And then, to get the invariance of several point sets in topological space. The main content of this paper is as following:The first chapter is a brief introduction of the development of dynamic system and the literature review at home and abroad. And then it gives the research content of this paper; the second chapter is mainly about the relevant concepts and theories in interval self-mapping and topological space, and then it introduces the definition and lemma of the descendible mapping; the third chapter mainly studies the invariance and the invariance of the iterative of periodic point set, eventually periodic point set,almost periodic point set and asymptotic periodic point set in one-dimensional interval self-mapping and descendible n-dimensional self-mapping; and then the relationship among the sets of point; the fourth chapter tests the invariance and relations of some point sets in metric space and topological space; The last chapter gives the summary and prospect.