On Correlation Research Of Sequence And Limit System In Strong Uniform Convergence

In this paper, we use two kinds of convergence (uniform convergence, strong uniform convergence)to study the relevance of sequence map and limit map. Under condition of the strong, the dynamic characteristics of sequence map about non wandering point, chaotic Devaney and Li-Yorke initial sensitivity can keep to the limit map. The main contents are as follows:The first chapter, as the introduction of this article, firstly introduces the origin of the topological dynamical system, and then introduces the related domestic and overseas research. At last, this article makes a simple introduction for framework.The second chapter, under the condition of uniform convergence, discuss wandering point to draw a conclusion that the sequence map can’t keep to the limit map. On this basis, introducing than consistent Convergence is stronger convergence. under the condi-tion of strong uniform convergence, the dynamic characteristics of wandering sequence map of point can keep to the limit map. Then we will study the set relation between the sequence map of wandering point and the limit map of wandering point:the limitation of the sequence of no-wander point supremum is included to the limit map.The third chapter will promote the strong uniform convergence from space to the hyperspace. It discusses three aspect. The first part discusses Devaney chaos between space and hyperspace, obtaining that if f is Devaney chaos, the cycle dense f is Devaney chaos. The second part, under the condition of uniform convergence, proves that if the sequence map is Devaney chaos, its limit map is Devaney chaos mapping. Under the condition of strong uniform convergence, the third part mainly discusses that the sequence map is Li-Yorke initial sensitivity, its limit map also is Li-Yorke initial sensitivityIt gives us a effective way to study dynamic character in a general dynamic system of (K(X),H).