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.
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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2004年第6期1237-1242,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10071022)
关键词
局部坐标
异宿环
同宿环
Local coordinates
Heteroclinic loop
Homoclinic loop
