局部紧致度量空间的渐进稳定集  

Asymptotically Stable Set of Local Compact Metric Space

作　　者：符子晴 霍展福 

机构地区：[1]广西大学,数学与信息科学学院,广西南宁

出　　处：《理论数学》2019年第2期230-236,共7页Pure Mathematics

摘　　要：设X为局部紧致度量空间,f:X→X是同胚映射。本文主要证明如下两个结论:1) 若对?x∈X,ω(x)≠?,K?X为紧致强不变集,且存在一个紧致邻域Q,使得Q\K包含不完整负轨道,则K是渐进稳定集;2) 若X的每一个有界闭集都是紧致的,且K?X为吸引子,则是渐进稳定的,其中与K有相同的吸引域。更多的,K是渐近稳定的当且仅当=K 。结论1),2)分别是对文献[1]和[2]中的结论进行了进一步推广。Let X be a local compact metric space, f:X→X be a homeomorphism.This article mainly proves the following two conclusions:1)Assume that K?X is a compact strongly invariant set and there exists a compact neighborhood K?X,such that Q\K contains no complete negative trajectory for every x∈X andω(x)is nonempty set,then K is asymptotically stable.2)If each bounded closed set is a compact set for X and let K?X be an attractor.Then is asymptotically stable with the same basin of attraction that K.Moreover K is asymptotically stable if only if=K.

关 键 词：渐进稳定集 不完全负轨道 吸引子 吸引域 

分 类 号：O1[理学—数学]