Research On Severl Kinds Of Entropy Of Continuous Map

In this dissertation, we give some kinds of new definitions about entropy, such as sequence points entropy, sequence pre-image entropy, sequence bundle-like pre-image entropy and sequence pre-image conditional metric entropy, and talk about the property of them respectively. This dissertation is composed of six chapters.In chapter one, we briefly and systematically introduce the background of entropy, status of entropy and main results of this dissertation.In chapter two, we briefly introduce some definitions of entropy that was given by previous mathematicians.In chapter three, we firstly define the definitions of sequence point’s entropy and sequence pre-image entropy. And then we prove the inequality of sequence points, sequence pre-image entropy and topological sequence entropy.In chapter four, we firstly define sequence pseudo-orbits entropy and sequence periodic pseudo-orbits entropy. And we prove that:(1) topological sequence entropy less or equal to sequence pseudo-orbits entropy and when we take A=(ti:i=1,2,...) as a special positive integer provide that tm+tn=tm+n, then hA(f)=t1h(f).(2) When we take A=(ti:i=1,2,...)as a special positive integer provide that tm+tn=tm+n, then topological sequence entropy less or equal to sequence periodic pseudo-orbits entropy and hA(f)=t1H(f). In chapter five, we firstly define sequence bundle-like pre-image entropy and prove that sequence bundle-like pre-image entropy is conjugate invariants and we have product rule of sequence bundle-like pre-image entropy. Moreover, when we take A=(ti:i=1,2,...) as a special positive integer provides that tm+tn=tm+n, then we have power rule.In chapter six, we first give the definition of sequence pre-image conditional measure-theoretic entropy and obtain product rule. When we take A=(ti:i=1,2,...) as a special positive integer provides tha tm+tn=tm+n, then we have power rule.