| 三点粗异宿环分支 |
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| 引用本文： | 金银来,朱德明.三点粗异宿环分支[J].数学学报,2004,47(6):1237-124. |
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| 作者姓名： | 金银来 朱德明 |
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| 作者单位： | 1. 临沂师范学院数学系,临沂,276005;华东师范大学数学系,上海,200062
2. 华东师范大学数学系,上海,200062 |
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| 基金项目： | 国家自然科学基金资助项目(10071022) |
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| 摘 要： | 本文研究高维系统连接三个鞍点的粗异宿环的分支问题.在一些横截性条件和非扭曲条件下,获得了Γ附近的1-异宿三点环, 1-异宿两点环、 1-同宿环和1-周期轨的存在性,唯一性和不共存性.同时给出了分支曲面和存在域.上述结果被进一步推广到连接l个鞍点的异宿环的情况,其中l≥2.
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| 关 键 词： | 局部坐标 异宿环 同宿环 |
| 文章编号： | 0583-1431(2004)06-1237-06 |
Bifurcations of Rough Heteroclinic Loops with Three Saddle Points |
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| Yin Lai JIN.Bifurcations of Rough Heteroclinic Loops with Three Saddle Points[J].Acta Mathematica Sinica,2004,47(6):1237-124. |
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| Authors: | Yin Lai JIN |
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| Institution: | Yin Lai JIN
(Department of Mathematics, Linyi Teachers' University, Linyi 276005, P. R. China) (Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China) De Ming ZHU (Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China) |
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| Abstract: | In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and noncoexistence of the 1-heteroclinic loop with three or two saddle points, the 1-homoclinic loop and 1-periodic orbit near Γ are obtained. Meanwhile, the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the case for heteroclinic loop with l saddle points. |
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| Keywords: | Local coordinates Heteroclinic loop Homoclinic loop |
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