非游荡半群及其性质

The Property of Nonwandering Semigroup

动力系统研究中 ,非游荡算子是在超循环算子研究的基础上 ,结合双曲不变性提出的一类性质较好的算子 而半群也是正被广泛研究的课题 ,在微分方程研究中尤其突出 W .Desch等人在超循环算子与半群的研究中提出了超循环半群的概念 ,并找到了一些微分方程的解半群具有这些性质 文献 [4 ]中 ,他给出了半群超循环以及混沌的充分条件 在他们的启发下 ,提出非游荡半群的概念 ,并在一些混沌半群中找到具体例子 。

In the research of dynamic system, nonwandering operator is a kind of 'good' operator. The work is based on the study of hypercyclic operator, and is combined with the hyperbolic invariant set. Simultaneously, semigroup are widely studied, especially in the study of Partial Differential Equations. In this paper we give the concept of the nonwandering semigroup, and show some concrete examples in the chaotic semigroup, so that we can broaden the study of hypercyclic operator.