Study Of Several Points Relevant Problems In Topology Dynamical System

Continuous mappings periodic point, recurrent point, non-wandering points andω limit points are the important research contents of topology power system. In recentyears, scholars at home and abroad are very interested in this field and have beenactively involved in the researches. They discussed the generalized periodic points onreal segment, even metric space and got a lot of important research results. However,with the modern dynamic system constantly developing to high-dimensional space andabstract space, some questions turn up:(1) How to put power system the periodic point, recurrent point, non-wanderingpoints, ω limit points and its related theory to the topological space?(2) What the relation between the periodic point, recurrent point, non-wanderingpoints, ω limit points, and what are the special nature of them?This paper did some researches about those problems and got some results, and itdivided into four chapters:Chapter One briefly introduce the topological dynamical systems of several pointsof the current situation and the main contents of this study.Chapter Two first refers to the basic concept of Topology power system and thenlists the concepts of the periodic point, recurrent point, non-wandering points andω limit points followed by the introduction of correlative characteristics.Chapter Three discusses the conclusions of the periodic point, recurrent point,non-wandering points and ω limit points.Chapter four is the conclusion and the recommendation.The results above caters to and promote the basic topological power systemtheories of the periodic point, recurrent point, non-wandering points,ω limit pointslay the theoretical foundation of abstract development in dynamical systems theory andtopology promotion in chaos mathematical theory.