Topological Structure of Non-wandering Set of a Graph Map  

作　　者：Rong Bao GU Tai Xiang SUN Ting Ting ZHENG 

机构地区：[1]School of Finance, Nanjing University of Finance and Economics, Nanjing 210046, P. R. China [2]Department of Mathematics, Guangxi University, Nanning 530004, P. R. China [3]Department of Mathematics, University of Science and Technology of China [4]Department of Mathematics, Anhui University, Hefei 230039, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2005年第4期873-880,共8页数学学报（英文版）

基　　金：NSF of the Committee of Education of Jiangshu Province of China (02KJB110008);supported by NNSF of China(19961001);the Support Program for 100 Young and Middle-aged Disciplinary Leaders in Guangxi Higher Education Institutions

摘　　要：Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.

关 键 词：Graph map Recurrent point ω-limit point Non-wandering set Derived set 

分 类 号：O15[理学—数学]