| 线性序拓扑空间上不稳定流形的映射性质 |
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| 引用本文： | 卢天秀,朱培勇.线性序拓扑空间上不稳定流形的映射性质[J].四川理工学院学报(自然科学版),2009,22(4):32-34. |
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| 作者姓名： | 卢天秀 朱培勇 |
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| 作者单位： | 1. 四川理工学院理学院,四川,自贡,643000
2. 电子科技大学应用数学学院,成都,610054 |
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| 基金项目： | 国家自然科学基金资助 |
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| 摘 要： | 文章研究完备稠序的线性序拓扑空间上连续自映射f的不稳定流形。首先证明了不动点P的不稳定流形与P的任意邻域V的交集,通过f有限次迭代之后,会包含P的不稳定流形。然后利用此结果证明了f~k在p_i(1≤i≤k)的不稳定流形被f映射的象集合为f~k在f(p_i)的不稳定流形(其中p_i为f的k-周期轨上的点)。
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| 关 键 词： | 线性序拓扑空间 不稳定流形 周期点 连续自映射 |
Features of Mapping of a Unstable Manifold on Linear Ordered Topological Space |
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| LU Tian-xiu,ZHU Pei-yong.Features of Mapping of a Unstable Manifold on Linear Ordered Topological Space[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2009,22(4):32-34. |
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| Authors: | LU Tian-xiu ZHU Pei-yong |
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| Institution: | 1.School of Science;Sichuan University of Science & Engineering;Zigong 643000;China;2.School of Applied Mathematics;University of Electronic Science and Technology of China;Chengdu 610054;China |
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| Abstract: | In this paper,the unstable manifold of a continuous self-mapping/on a completely densely ordered linear ordered topological space is discussed.First of all,it is proved that the intersection of the unstable manifold of a fixed point p and arbitrary neighborhood of point p,by the finite iteration of f,will contains the unstable manifold of point p.Then,by using of the above conclusion,the following result is obtained.f maps the unstable manifold of f~k at p_i(1≤i≤k) to the unstable manifold of f~k at f(p_i)(p_i is a point in periodic orbit with period k of f). |
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| Keywords: | linear ordered topological space unstable manifold periodic point continuous self-mapping |
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