| 树映射的链回归点与拓扑熵 |
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| 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. DOI: 10.1007/s11766-002-0010-1 |
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| 作者姓名： | 孙太祥 |
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| 作者单位： | Dept.ofMath.,GuangxiUniv.,Nanning530004 |
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| 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) |
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| 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.
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| 关 键 词： | 树 映射 链回归点 拓扑熵 |
| 收稿时间： | 2001-10-29 |
Chain recurrent points and topological entropy of a tree map |
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| 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. DOI: 10.1007/s11766-002-0010-1 |
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| Authors: | Sun Taixiang |
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| Affiliation: | (1) Dept. of Math., Guangxi Univ., 530004 Nanning;(2) Dept. of Math., Univ. of Science and Technology of China, 230026 Hefei, China |
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| 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). |
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| Keywords: | tree map division chain recurrent point topological entropy the set of chain equivalent points. |
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