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

共 15 条

[1]

[Anonymous], 1995, QUALITATIVE THEORY P

[2]

CAI SL, 1992, PROCEEDINGS OF ASIAN MATHEMATICAL CONFERENCE 1990, P25

[3]

Feng B, 1985, Acta Math Sinica, V28, P53

[4]

GUCKENBEIMER J, 1983, NONLINEAR OSCILLATIO

[5]

HAN M, 1993, SCI CHINA SER A, V23, P113

[6]

Han M., 1994, Bifurcation Theory of Differential Equation

[7]

HAN M, 1994, SCI CHINA SER A, V37, P1152

[8] ON SADDLE-LOOP BIFURCATIONS OF LIMIT-CYCLES IN PERTURBATIONS OF QUADRATIC HAMILTONIAN-SYSTEMS [J].

HOROZOV, E ;

ILIEV, ID .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 113 (01) :84-105

[9]

ILIEV I, ADV DIFF EQS, V1, P689

[10] SADDLE QUANTITIES AND APPLICATIONS [J].

JOYAL, P ;

ROUSSEAU, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 78 (02) :374-399

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