Devaney Chaotic Semigroup Action

Chaos is the properly peculiarly stste of non-liner dynamical system.Now,there are many methods to study character about chaos.One of these methods is using the thoughtway of analysissitus that can avoid complitated count.So,this is a powerful tool to study chaos theory.Our basic objective in this paper is to study the peculiarly topological configuration and character.Mostimportant,this paper import the action of group into topological space to looking for the way opening to chaos.In chapter one,we introduce simply the development about dynamical system and the background of this paper.In chapter two,we study mainly the connection of the Li-Yorke's scrambled set and non-wandering set that recruits Li-York theorem.We gain some characters of transitive dynamical system and proof theorem as follows:if dynamical system(X,f)has a period point,then f has a Li-Yorke's scrambled set S made up of non-wandering points.In chapter three,we define Devaney chaos of semigroup action by importing the action of semigroup action into topological space:if semigroup S continuously acts on the inverse limit space X.At the same time,it must satisfy conditions as follows:(1) topologically transitive;(2)sensitive dependence on initial condition.Then,this semigroup action is Devaney chaos.In addtion,it gives several equivalent propositions of topologically transitive and the connection with topologically strong mixing in the sence of semigroup action.In chapter four,first we summarize the results in this thesis,then we analyze the questions that exist in this studying and show the direction of studying that we will do in future.