三点粗异宿环分支  

Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

作　　者：金银来[1] 朱德明[2] 

机构地区：[1]临沂师范学院数学系,临沂276005 [2]华东师范大学数学系,上海200062

出　　处：《数学学报（中文版）》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)

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.

关 键 词：局部坐标 异宿环 同宿环 

分 类 号：O175.12[理学—数学]