| 关于逐点伪轨跟踪性的研究 |
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| 引用本文： | 黎日松,吴华明.关于逐点伪轨跟踪性的研究[J].广东海洋大学学报,2007,27(1):64-68. |
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| 作者姓名： | 黎日松 吴华明 |
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| 作者单位： | 1. 广东海洋大学理学院,广东,湛江,524025
2. 湛江师范学院数学与计算学院,广东,湛江,524048 |
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| 基金项目： | 衷心感谢左再思教授、沈文淮教授和代雄平副教授的热情鼓励及提供有益建议. |
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| 摘 要： | 设X和～X为度量空间,且X是紧致的,f是X上连续自映射,证明了:若fk有PWPOTP(PWPOTP+),则f有PWPOTP(PWPOTP+);满射f有PWPOTP(PWPOTP+)当且仅当由(X,f)生成的逆极限系统(Xf,σf)上转移自映射σf有PWPOTP(PWPOTP+);PWPOTP(PWPOTP+)是拓扑共轭不变性;设f,g分别为X～和X上自同胚(自映射),π∶～X→X为局部等距覆盖映射,且πf=gπ,若有δ0>0,使对x～∈～X和δ>0(δ≤δ0),x～的半径为δ的开球Uδ(x～)连通,且πUδ(x～)为等距映射,则f有PWPOTP(PWPOTP+)当且仅当g有PWPOTP(PWPOTP+);恒等映射id有PWPOTP当且仅当X是完全不连通的。
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| 关 键 词： | 伪轨跟踪性 逐点伪轨跟踪性 链可迁 |
| 文章编号： | 1673-9159（2007）01-0064-05 |
| 修稿时间： | 2006-05-20 |
Research on Pointwise Pseudo-orbit Tracing Property |
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| LI Ri-song,WU Hua-ming.Research on Pointwise Pseudo-orbit Tracing Property[J].Journal of Zhanjiang Ocean University,2007,27(1):64-68. |
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| Authors: | LI Ri-song WU Hua-ming |
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| Institution: | 1. Faculty of sciences, Gnangdong Ocean University, Zhanjiang, 524088, China ; 2. School of Mathematics and Computational scionce, Zhanfing Normal ollege, Zhanjiang, 524048, China |
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| Abstract: | Let X and X be metric spaces and X be compact, and let f be a continuous map from X to itself. In this paper, the following statements were proved: If fk has PWPOTP(PWPOTP+),then f has PWPOTP(PWPOTP+);Let f be a surjection and (Xf,df) be the inverse limit space generated by (X,f),and σf be the shift map on Xf.then f has PWPOTP(PWPOTP+)if and only if σf has PWPOTP(PWPOTP+);PWPOTP(PWPOTP+)is an invariant property under topological conjugation;Let f∶X → X and g∶X → X be homeomorphisms (continuous maps), and π∶X → X be a locally isometric covering map such that π°f=g°π.If there exists δ0>0 such that for each x∈ X and δ>0(δ≤δ0) the open ball Uδ(x) of x with radius δ is connected and π│Uδ(x) is an isometry,then f has PWPOTP(PWPOTP+)if and only if g has PWPOTP(PWPOTP+); The identity map id has PWPOTP if and only if X is totally disconnected. |
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| Keywords: | Pseudo-orbit tracing property Pointwise pseudo-orbit tracing property Chaintransitive |
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