作　　者： ;

机构地区： 合肥学院数学与物理系

出　　处： 《阜阳师范学院学报（自然科学版）》 2014年第2期9-11,共3页

摘　　要： 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.

关 键 词： 动力系统 轨道 极限集 不变集

领　　域： [理学] [理学]