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数学进展
研究论文
树映射的单侧γ-极限点集与拓扑熵
The Set of Unilateral 7-limit Points and the Topological Entropy of a Tree Map

孙太祥
SUN Tai-xiang

广西大学数学系 南宁,广西, 530004 汕头大学数学所,汕头,广东, 515063
(1. Department of Mathematics, Guangxi University, Nanning, Guangxi, 530004, P. R. China; 2. Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, P. R. China

收稿日期: 2004-02-25
出版日期: 2004-02-25

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摘要 本文讨论了树映射的单侧γ-极限点集与吸引中心的关系,得到了树映射具有正拓扑熵的几个等价条件.此外,还得到了树映射是强非混沌以及逐片单调树映射的拓扑熵为零的几个等价条件.
关键词 树映射单侧γ-极限点拓扑熵强非混沌逐片单调树映射    
Abstract:In the present paper we discuss the relation between the set of unilateral 7-limit points and the attracting centre of a tree map, and obtain a few equivalent conditions which a tree map has positive topological entropy. Furthermore, we also obtain a few equivalent conditions which a tree map is strongly not-chaotic and a few equivalent conditions which a piecewise monotone tree map has topological entropy zero.
Key words unilateral 7-limit point    topological entropy    strongly not-chaos    piecewise monotone tree map
[1] 尹建东,杨忠选. 关于拟弱几乎周期点的一些结论和公开问题[J]. 数学进展, 2014, 43(3): 321-328.
[2] 孙太祥,席鸿建,陈占和,张永平. 图映射的吸引中心与拓扑熵[J]. 数学进展, 2004, 33(5): 540-546.
[3] 胡骏. Feigenbaum刚性和界于简单与混沌之间的动力系统(英文)[J]. 数学进展, 1998, 27(5): 0-0.
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