| 圆周上连续自映射非游荡点集的拓扑结构 |
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| 引用本文： | 杨景春,王清燕. 圆周上连续自映射非游荡点集的拓扑结构[J]. 吉林大学学报(理学版), 1996, 0(4) |
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| 作者姓名： | 杨景春 王清燕 |
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| 作者单位： | 吉林师范学院数学系，吉林大学数学系 |
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| 摘 要： | 给出了圆周Ｓ１上连续自映射ｆ，Ｐ（ｆ）≠的如下结果：（１）如果ｘ∈Ｗ（ｆ）－Ｐ（ｆ），则ｘ的轨道是无限集；（２）ｆ的每个孤立的周期点都是ｆ的孤立非游荡点；（３）ｆ非游荡点集的每个聚点都是ｆ的周期点集的二阶聚点；（４）ｆ的ω极限点集的导集等于ｆ周期点集的导集；ｆ的非游荡点集的二阶导集，等于ｆ的周期点集的二阶导集．
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| 关 键 词： | 非游荡点，孤立周期点，α－极限点 |
Topological Structure of Nonwandering Sets of Continuous Self-Maps of the Circle |
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| Yang Jingchun. Topological Structure of Nonwandering Sets of Continuous Self-Maps of the Circle[J]. Journal of Jilin University: Sci Ed, 1996, 0(4) |
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| Authors: | Yang Jingchun |
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| Abstract: | For a continuous map f of the circle SI to itself, we show=(1 ) If x6 W(f) --p(f),then the orbit of x is infinite set.(2) Each isolated periodic point of f is an isolated nonwandering point of f.(3) Every condensation point of O(f) is the condensation point of two order of p(f).(4) The set of condensation points of W(f)equals to the set of condensation points of p(f). The set of condensation points of two order of n(f)equals to the set of condensation points of two order of P(f). |
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