On The Variational Principle For The Topological Entropy Of Non-compact Set

In this thesis,we discuss the topological entropy for noncompact sets.The main content as follows:In chapter 2,we study the discrete case.For a continuous transformation T of a compact spaces (X, d), we consider the set of the formwe get Variational Principle is the topo logical entropy for noncompact sets,(T) is the usual measure theoretic entropy.In fact ,we prove the equation .In chapter 3,we introduce the definition of the topological entropy for flows on noncompact sets,and by using the topological entropy ,we define the measure theoretic entropy for flows.We get the relation between topological entropy ?measure theoretic entropy and the usual entropy of time-one map.And by establishing the Variational Principle between topological entropy and measure theoretic entropy,we conclude that the topological entropy which is defined by us is equivalent to Sun Wenxiang's definition.