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| Topological Structure of Non-wandering Set of a Graph Map | |
| 引用本文： | Rong Bao GU Tai Xiang SUN Ting Ting ZHENG. Topological Structure of Non-wandering Set of a Graph Map[J]. 数学学报(英文版), 2005, 21(4): 873-880. DOI: 10.1007/s10114-004-0432-1 |
| 作者姓名： | Rong Bao GU Tai Xiang SUN Ting Ting ZHENG |
| 作者单位： | [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 |
| 基金项目： | The first author is supported by NSF of the Committee of Education of Jiangshu Province of China （02KJB110008）, and the second author is supported by NNSF of China （19961001） and 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. |
| 关 键 词： | 拓扑结构 非游荡集 图形映射 导集 循环点 |
| 收稿时间： | 2002-05-14 |
| 修稿时间： | 2002-05-142003-04-17 |
Topological Structure of Non–wandering Set of a Graph Map |
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| Rong Bao Gu,Tai Xiang Sun,Ting Ting Zheng. Topological Structure of Non–wandering Set of a Graph Map[J]. Acta Mathematica Sinica(English Series), 2005, 21(4): 873-880. DOI: 10.1007/s10114-004-0432-1 | |
| Authors: | Rong Bao Gu Tai Xiang Sun Ting Ting Zheng |
| Affiliation: | (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, Hefei 230026, P. R. China;(4) Department of Mathematics, Anhui University, Hefei 230039, P. R. China |
| Abstract: | 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. The first author is supported by NSF of the Committee of Education of Jiangshu Province of China (02KJB110008), and the second author is supported by NNSF of China (19961001) and the Support Program for 100 Young and Middle–aged Disciplinary Leaders in Guangxi Higher Education Institutions |
| Keywords: | Graph map Recurrent point ω – limit point Non– wandering set Derived set |
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