Study Of Invariant Subset Of Some Self-maps In Topological Systems

Let X is a topological space,f∈C0(X,X),Let f0 is the identity map,and define f1=f,f2=f(?)f,…,fn=f(?)fn-1 inductively for n≥1.The sequence of maps f0,f1, f2,..., is called the dynamical system for map fTopological system in one dimension is compact one- dimensional connected manifold that is the theory on continuous self-maps of the interval and the circle. It is the simplest dynamical system and is an important direction of topological dynamical systems The study of invariant subset is very important in the dynamical system,because, in the corresponding physical or other meaningful process of change, the elements of invariant subset elements corresponding to the state, often not those who disappear without reproduction of the insignificant moments of "transient", but people are concerned about the so-called the non-escape condition, that is, "constant state".Periodic orbit is the simplest invariant subset, we studied the more general invariant subset:periodic point,recurrent point,wlimiting point,Non-wandering point as well as the chain recurrent point and so on. The relationship between the set of points, as well as the behavior of map on the set of points profoundly reveals the properties of dynamical system for map.This thesis promotes the invariant subset on topological system in one dimension dependence on initial value and extends the scope of dynamical system,which better reflect the intrinsic nature of the system and lay a theoretical foundation for the future application. The main contents of this paper are follows:The study on dimensional manifold dynamic system in the higher (continuous or discrete) have a number of very complex phenomenon, these phenomena are more hope that have been clarified on dimensional manifold dynamic system in the more lower and the more simpler. So the descendible can be reduced in this article.We know that the invariant subset are generated by mapping iteration and the predecessors have already seen the periodic point is iterative in the research of self-maps of the interval.This article will be extended to the n-dimensional descendible continuous self-mapping.Self-maps of the circle as interval for complex iterated space, each self-maps of the circle as self-maps of the interval for promotion. This allows us to study self-maps of the circle by self-maps of the interval.In this paper, the use of the article [17] giving the concept on imitative exponential mapping and promotion from invariant subset of self-maps of the interval attributed to the self-maps of circle.