不可逆离散动力系统的抽象ω-极限集

ABSTRACT ω-LIMIT SETS FOR SEMI-DYNAMICAL SYSTEMS

R.Bowen 对于紧致度量空间上的可逆离散动力系统(即自同胚的双向迭代列)引入了抽象ω-极限集的概念,并得到了一些有意义的性质.作为推广,本文对紧致度量空间上的由自映射的正向迭代形成的不可逆离散动力系统定义了抽象ω-极限集,随后证明了两个等价条件.这些条件清楚地刻划了这种极限集的动力学意义.

In this paper,for semi-dynamical system two conditions equivalent to the notion of ab-stract ω-limit set introduced by Bowen in 19755 are presented.It is proved that,if an invar-iant set ∧(?)Ω(f) for an Axiom A self-cover-mapping is an abstract ω-limit set,then thereis an x∈[Ω(f)]~f so that ∧=ω(x)=α(x).A result about the problem of basic neighborhoodfor the self-cover-mappings is also presented.