ω-Limit Set of a Tree Map  

作　　者：曾平凡 莫红 郭文旌 高文旌 

机构地区：[1]Institute of Mathematics, Guangxi University, Nanning, 530004

出　　处：《Northeastern Mathematical Journal》2001年第3期333-339,共7页东北数学（英文版）

基　　金：The NSFC(19961001) and the NSF(9811022) of Guangxi.

摘　　要：Let T be a tree and f be a continuous map from T into itself. We show mainly in this paper that a point x of T is an w-limit point of f if and only if every open neighborhood of x in T contains at least nx + 1 points of some trajectory, where nx equals the number of connected components of T \ {x}. Then, for any open subset G w(f) in T, there exists a positive integer m = m(G) such that at most m points of any trajectory lie outside G.This result is a generalization of the related result for maps of the interval.Let T be a tree and f be a continuous map from T into itself. We show mainly in this paper that a point x of T is an w-limit point of f if and only if every open neighborhood of x in T contains at least nx + 1 points of some trajectory, where nx equals the number of connected components of T \ {x}. Then, for any open subset G w(f) in T, there exists a positive integer m = m(G) such that at most m points of any trajectory lie outside G.This result is a generalization of the related result for maps of the interval.

关 键 词：periodic point ω-limit point TREE 

分 类 号：O192[理学—数学]