| 引用本文： |
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张更容,曾凡平,秦斌.区间[0,1)上每个点都为链回归点的映射[J].广西科学,2007,14(2):95-97,102. [点击复制]
- ZHANG Geng-rong,ZENG Fan-ping,QIN Bin.Maps of the Interval[0, 1) with Every Point Chain Recurrent[J].Guangxi Sciences,2007,14(2):95-97,102. [点击复制]
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| 摘要: |
| 设X=[0,1),f:X→X是连续自映射.指出:如果f是逐点链回归的(也就是说,X中的每一点在f下是链回归的),那么,若Fix(f)是连通的,则f是恒等映射;若Fix(f)是不连通的,则f含湍流. |
| 关键词: 区间映射 逐点链回归 湍流 |
| DOI： |
| 投稿时间：2006-09-21修订日期：2007-01-26 |
| 基金项目:Supported by NSFC (10661001); Guangxi Science Foundation(0640002);the Innovation Project of Guangxi Graduate Education(2006105930701M14);Science Foundation of Guangxi University(X061022). |
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| Maps of the Interval[0, 1) with Every Point Chain Recurrent |
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ZHANG Geng-rong1, ZENG Fan-ping1,2, QIN Bin1
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| (1.Department of Mathematics and Information Sciences, Guangxi University, Nanning, Guangxi, 530004, China;2.Department of Mathematics, Liuzhou Teachers College, Liuzhou, Guangxi, 545004, China) |
| Abstract: |
| Let X=[0, 1), f:X→X be a continuous map. It is showed that if f is pointwise chain recurrent (that is, every point of X is chain recurrent under f), then f is identity if Fix (f) is connected;f is turbulent if Fix (f) is disconnected. |
| Key words: interval maps pointwise chain recurrent turbulent |
