| 树映射的链回归点与拓扑熵 |
| |
| 引用本文： | 孙太祥.树映射的链回归点与拓扑熵[J].高校应用数学学报(英文版),2002,17(3):313-318. |
| |
| 作者姓名： | 孙太祥 |
| |
| 作者单位： | Dept.ofMath.,GuangxiUniv.,Nanning530004 |
| |
| 基金项目： | the National Natural Science Foundation of China(1 996 1 0 0 1 ) and SF of Guangxi(0 1 3 5 0 2 7) |
| |
| 摘 要： | Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) fhas zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f^5 has a division; (2) If f has zero topological entropy,then for any xECR(f)--P(f) the w-limit set of x is an infinite minimal set.
|
| 关 键 词： | 树 映射 链回归点 拓扑熵 |
| 收稿时间： | 29 October 2001 |
Chain recurrent points and topological entropy of a tree map |
| |
| Sun?Taixiang.Chain recurrent points and topological entropy of a tree map[J].Applied Mathematics A Journal of Chinese Universities,2002,17(3):313-318. |
| |
| Authors: | Sun Taixiang |
| |
| Institution: | (1) Dept. of Math., Guangxi Univ., 530004 Nanning;(2) Dept. of Math., Univ. of Science and Technology of China, 230026 Hefei, China |
| |
| Abstract: | Let f be a tree map, P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper, the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) f has zero topological entropy if and only if for any xε CR(f)−P(f) and each natural number s the orbit of x under f
s
has a division; (2) If f has zero topological entropy, then for any x ε CR(f) − P(f) the θ-limit set of x is an infinite minimal set.
Supported by the National Natural Science Foundation of China (19961001) and SF of Guangxi (0135027). |
| |
| Keywords: | tree map division chain recurrent point topological entropy the set of chain equivalent points |
| 本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录！ |
