| 一类连续体上连续映射的周期点 |
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| 引用本文： | 孙太祥,顾荣宝. 一类连续体上连续映射的周期点[J]. 数学学报, 2004, 47(2): 343-348. DOI: cnki:ISSN:0583-1431.0.2004-02-016 |
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| 作者姓名： | 孙太祥 顾荣宝 |
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| 作者单位： | 1. 广西大学数学系,南宁,530004;中国科学技术大学数学系,合肥,230026
2. 南京经济学院应用数学系,南京,210003;安徽大学数学系,合肥,230039 |
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| 基金项目： | 国家自然科学基金(10361001)，广西科学基金(0135027)，广西高校百名中青年学科带头人资助计划，江苏省教育厅自然科学基金资助项目 |
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| 摘 要： | 设X是个阶有限的遗传可分解可链连续体, f:X→X是X上的连续自映射, On(x,f)={fi(x):0≤i≤n)是f的一个返回轨道, inf(On(x,f))
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| 关 键 词： | 遗传可分解可链连续体 返回轨道 向心点 周期点 |
| 文章编号： | 0583-1431(2004)02-0343-06 |
On Periodic Points of Continuous Maps of a Class of Coutinua |
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| Tai Xiang SUN. On Periodic Points of Continuous Maps of a Class of Coutinua[J]. Acta Mathematica Sinica, 2004, 47(2): 343-348. DOI: cnki:ISSN:0583-1431.0.2004-02-016 |
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| Authors: | Tai Xiang SUN |
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| Affiliation: | Tai Xiang SUN(Department of Mathematics, Guangxi University, Nanning 530004, P. R. China)(Department of Mathematics, University of Science and Technology of China,Hefei 230026, P. R. China)Rong Bao GU(Department of Applied Mathematics, Nanjing University of Economics,Nanjing 210003, P. R. China) (Department of Mathematics, Anhui University, Hefei 230039, P. R. China) |
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| Abstract: | Let X be a hereditarily decomposable chainable continuum with finite order, f : X → X be a continuous self-map of X, On(x, f) = {fi(x) : 0 ≤ i ≤ n} be a return trajectory of f, and inf{On(x, f)} < p - f(p) < sup{On(x, f)}. In this paper, we prove that if there exist k centripetal points of f in {fi(x) : Q ≤ i ≤ n - 1} relative to p, then f has periodic points with some odd period 1 < R ≤ (n - 2)/k + 2. |
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| Keywords: | Hereditarily decomposable chainable continuum Return trajectory Centripetal point Periodic point |
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