非混沌的树映射  

NON-CHAOTIC TREE MAPS

作　　者：孙太祥[1] 顾荣宝[2] 张永平[1] 

机构地区：[1]中国科学技术大学数学系 [2]南京经济学院应用数学系

出　　处：《数学年刊（A辑）》2004年第1期113-122,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10361001;10226014);广西高校百名中青年学科带头人资助的项目

摘　　要：设f是树T上的连续自映射,SAP(f),ω(f);Ω(f)分别是f的强几乎周期点集,ω-极限集,非游荡集.本文证明下面几条是等价的:(i)f是非混沌的;(ii)SAP(f)=ω(f);(iii)fΩ(f)是逐点等度连续的;(iv)f│ω(f)是逐点等度连续的;(v)f是一致非混沌的。Let f be a continuous self-map of a tree T, and SAP(f), w(f),Ω(f) be the set of strongly almost periodic points of f, the set of w-limit points of /, the set of non-wandering points off/ respectively. In this paper, the authors prove that the following statements are equivalent: (i)f is non-chaotic; (ii)SAP(f) = w(f); (iii)f|Ω(f) is pointwise equicontinuous; (iv)f|w(f) is pointwise equicontinuous; (v)f is uniformly non-chaotic.

关 键 词：树映射 非混沌 一致非混沌 等度连续 拓扑熵 

分 类 号：O415.5[理学—理论物理]