【作者】 刘恂；

【导师】 田立新；

【作者基本信息】 江苏大学 ， 应用数学， 2003， 硕士

【摘要】 本文将利用微分动力系统和泛函分析的方法，着重研究混沌动力学中的一类线性算子以及算子半群——非游荡算子半群。本文利用超循环算子和半群的性质和最新的研究进展，着眼于非游荡算子理论与超循环算子(及半群)、混沌算子(及半群)或者更一般的半群，结合各自定义建立之间联系。本文还将在特定的无穷维空间找出具体的非游荡算子半群例子，将给出非游荡算子半群的一个充分条件，且依照已有的结果和方法获得非游荡算子半群的超循环算子半群分解。并且在本文最后，还将结合多重超循环这一最新的理论来分析非游荡算子半群的超循环分解。 另一方面，本文将结合微分动力系统和拓扑动力系统的研究方法，主要从微分动力系统的角度，从根本上分析非游荡算子半群存在的条件，并结合与此密切相关的有限维空间的一些成熟的理论，如拓扑动力系统中的拓扑混合性等，从不同角度试图解决无穷维空间的结论。为同类的问题提供相近的思路。更多还原

【Abstract】 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.更多还原