不可分系统的Auslander-Yorke二分定理  

Auslander-Yorke dichotomy theorem for indecomposable systems

作　　者：陈志景[1] 黄煜[2] CHEN ZhiJing HUANG Yu

机构地区：[1]南京大学数学系,南京210093 [2]中山大学数学与计算科学学院,广州510275

出　　处：《中国科学：数学》2016年第11期1715-1726,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371380)资助项目

摘　　要：Auslander-Yorke二分定理阐述了一个传递系统要么是几乎等度连续的,要么是敏感的.称一个系统(X,f)是不可分的,如果X中的任意两个内部非空的f-不变闭子集都有公共的内点.不可分性严格弱于传递性.本文证明每一个满足f:X→X半开的不可分系统(X,f)要么是几乎等度连续的,要么是敏感的.进一步,在不可分的几乎等度连续系统中,所有等度连续点都有相同的ω-极限集.The Auslander-Yorke dichotomy theorem says that every transitive system is either sensitive or almost equicontinuous. A topological dynamical system （X, f） is said to be indecomposable if every two f- invariant closed subsets having non-empty interiors must have common interior points. This notion is strictly weaker than transitivity. In this paper, we show that every indecomposable system with f being semi-open is either almost equicontinuous or sensitive, which complements the Auslander-Yorke dichotomy theorem. Moreover, we prove that in an almost equicontinuous indecomposable system all equicontinuous points have the same ω- limited set.

关 键 词：传递 不可分 等度连续 敏感 

分 类 号：O189.11[理学—数学]