三点粗异宿环分支

金银来;朱德明

数学学报 ›› 2004, Vol. 47 ›› Issue (6) : 1237-124.

PDF(425 KB)
PDF(425 KB)
数学学报 ›› 2004, Vol. 47 ›› Issue (6) : 1237-124. DOI: 10.12386/A2004sxxb0156
论文

三点粗异宿环分支

    金银来;朱德明
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Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

    Yin Lai JIN, De Ming ZHU
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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.

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.

关键词

异宿环 / 局部坐标 / 同宿环

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金银来;朱德明. 三点粗异宿环分支. 数学学报, 2004, 47(6): 1237-124 https://doi.org/10.12386/A2004sxxb0156
Yin Lai JIN, De Ming ZHU. Bifurcations of Rough Heteroclinic Loops with Three Saddle Points. Acta Mathematica Sinica, Chinese Series, 2004, 47(6): 1237-124 https://doi.org/10.12386/A2004sxxb0156
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