关于序列紧空间上连续自映射的ω-极限点

ω-Limit Points of a Continuous Self-mapping on a Sequentially Compact Space

在一般拓扑空间上研究拓扑动力系统的轨道渐近性质.证明了以下结果:设X是序列紧空间,f是X上的连续自映射,点x的ω-极限集ω(x,f)为有限集当且仅当它是f的一个周期轨.作为推论,在紧空间和可数紧空间中也有完全相同的结果.

This paper discusses the orbital asymptotic properties of a topological dynamical system whose base space is a sequentially compact space, and proves the main theorem： Let f be a continuous self-mapping on a sequentially space X, then ω-limit set ω（x, f） of a point ：r∈X is a nonempty finite set if it is a periodic orbit of f. As inference, the authors get exactly the same conclusion when X is a compact （count- ably compact） space.