离散动力系统ω-极限集的一种不可分性及其应用

Inseparable property of ω-limit sets of discrete dynamical systems and its application

对紧致度量空间的自同胚映射所生成轨道的极限性态进行讨论。对离散动力系统,给出了ω-极限集不能表示为两个互不相交的非空闭不变子集的详细证明,并以此为基础得到ω-极限集为一个周期轨道的几个充分条件,在此过程中也得到了含有无限个元素的ω-极限集中周期轨道不含孤立点的一个充分条件。

The limit properties of the self-homeomorphism map on compact metric space were investigated. A detailed proof was obtained to show that a ω-limit Set can not be represented as the disjoint union of two closed invariable sets. As its application, several sufficient conditions are gained when a ω-limit Set is just a periodic orbit. At the same time, a sufficient condition is also ob-tained when a periodic orbit contained in infinite ω-limit Set does not contain any isolated point.