About Topological Entropy Research

On the century 60's intermediate stages for studies the Topology Dynamic System,by the Shannon entropy,the Kolmogorov entropy the analysis topological entropy concept which produces for the foundation,are about the analysis Topology Dynamic System in "not the determinism" mathematics measure.It is acting the important role in the modern dynamic system,Its computation is the question which the numerous mathematicians eagerly solves.This article is precisely believed based on this that,has made the more systematic summary to the Topology Dynamic System in about the entropy correlation definition and its the computation,then the structure new system carries on the computation to its analysis topological entropy,and further uses the entropy to come to carry on the division to the set.In first chapter briefly introduced the topological entropy history and its the function,and future prospects for development.In second chapter to the topological entropy,the topological equence entropy definition and the nature has carried on the more comprehensive system outline,and has done more thorough research to the topological sequence entropy nature.Has obtained about ent_A(f~m)=m·ent_A(f)establishment condition.In third chapter to had is number less topological entropy some results has carried on the iteration,and the topological entropy has carried on the computation to the mark space in,the latter structure C~*-algebra Dynamic System,again has carried on the computation to its topological entropy,Has obtained its topological entropy perhaps 0 perhaps∞.In fourth chapter has studiedα-entropy set:E~α(X,f),A brand-new concept. This chapter has carried on the discussion to its many nature,obtains:Under identical f,the topological space(X,f)entropy,α-entropy set E~α(X,f)entropy as well as the biggest entropy track(?)h((?),f)entropy is equal.