Properties Of Nonwandering Operator Semigroup

The paper will apply the methods of differential dynamical system and of functional analysis to the study of a series of linear operators and semigroup-nonwandering semigroup in chaotic dynamical system. The paper will utilize the properties and the latest work for hypercyclic operators and semigroups, and particularly for the theory of nonwandering operators, hypercyclic semigroups, and chaoticand semigroups. Combining their definitions, we will form their connections. In addition, in a certain infinite dimensional space, the paper will provide an example of nonwandering semigroup and a sufficient condition for nonwandering semigroup. According to recent results and methods, we may get the hypercyclic decomposition of nonwandering semigroup. And, we will discuss the hypercyclic decomposition from the multi-hypercyclic operator provided not long ago.In addition , the paper will analyze the existence condition for nonwanderingsemigroup by the methods of topological dynamical system. From the mature results of finite dimensional space, such as the topological mixing, we discuss any other methods to solve the problems of infinite dimensional space, so as to provide the similar methods for the similar work.