Cyclicity of planar homoclinic loops and quadratic integrable systems

被引：54

作者：

Han, MA

机构：

[1] Department of Mathematics, Shanghai Jiaotong University

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 1997年 / 40卷 / 12期

基金：

中国国家自然科学基金;

关键词：

homoclinic loop; bifurcation; limit cycle; cyclicity;

D O I：

10.1007/BF02876370

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general method for a homoclinic loop of planar Hamiltonian systems to bifurcate two or three limit cycles under perturbations is established. Certain conditions are given under which the cyclicity of a homoclinic loop equals 1 or 2. As an application to quadratic systems, it is proved that the cyclicity of homoclinic loops of quadratic integrable and non-Hamiltonian systems equals 2 except for one case.

引用

页码：1247 / 1258

页数：12