| tvs锥度量空间上同胚映射的可扩性 |
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| 引用本文： | 葛洵.tvs锥度量空间上同胚映射的可扩性[J].数学研究及应用,2016,36(3):363-368. |
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| 作者姓名： | 葛洵 |
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| 作者单位： | 苏州大学数学科学学院, 江苏 苏州 215006 |
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| 基金项目： | 国家自然科学基金(Nos.11301367;61472469;11461005),教育部博士学科点基金(No.20123201120001). |
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| 摘 要： | 设$f$是紧tvs锥度量空间上同胚映射. 本文证明了$f$是tvs锥可扩的当且仅当$f$有生成元. 进一步, 如果$f$是tvs锥可扩的,则具有收敛半轨的点集是可数集. 本文的这些结果改进了拓扑动力系统的一些可扩同胚定理, 将有助于研究tvs锥度量空间上同胚映射的动力性质.
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| 关 键 词： | tvs锥度量空间 tvs锥可扩同胚 生成元 收敛半轨 |
| 收稿时间： | 2015/3/20 0:00:00 |
| 修稿时间： | 3/8/2016 12:00:00 AM |
Expansive Behaviours for Homeomorphisms of tvs-Cone Metric Spaces |
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| Xun GE.Expansive Behaviours for Homeomorphisms of tvs-Cone Metric Spaces[J].Journal of Mathematical Research with Applications,2016,36(3):363-368. |
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| Authors: | Xun GE |
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| Institution: | School of Mathematical Sciences, Soochow University, Jiangsu 215006, P. R. China |
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| Abstract: | Let $f$ be a homeomorphism of a compact tvs-cone metric space. In this paper, we show that $f$ is tvs-cone expansive if and only if $f$ has a generator. Further, it is proved that if $f$ is tvs-cone expansive, then the set of points having converging semiorbits under $f$ is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces. |
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| Keywords: | tvs-cone metric space tvs-cone expansive homeomorphism generator converging semiorbit |
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