On the cyclicity of a 2-polycycle for quadratic systems

被引：8

作者：

Han, MA ^{[1
]}

Yang, C ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200030, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2005年 / 23卷 / 05期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1016/j.chaos.2004.07.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

lt has been already known that the maximum number of limit cycles near a homoclinic loop of a quadratic Hamiltonian system under quadratic perturbations is two. However, the problem of finding the maximum number of limit cycles in the 2-polycycle case is still open. This paper addresses the problem in some detail and solves it partially. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：1787 / 1794

页数：8

共 12 条

[1] The cyclicity of period annuli of degenerate quadratic Hamiltonian systems with elliptic segment loops [J].

Chow, SN ;

Li, CZ ;

Yi, YF .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 :349-374

[2]

DEJAGER P, 1989, THESIS TU DELFT

[3] ELEMENTARY GRAPHICS OF CYCLICITY-1 AND CYCLICITY-2 [J].

DUMORTIER, F ;

ROUSSARIE, R ;

ROUSSEAU, C .

NONLINEARITY, 1994, 7 (03) :1001-1043

[4]

HAN M, J DIFF EQS, V155, P245

[5] Cyclicity of planar homoclinic loops and quadratic integrable systems [J].

Han, MA .

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1997, 40 (12) :1247-1258

[6]

Han MA, 1999, SCI CHINA SER A, V42, P605

[7] 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

[8]

ILIEV I, 1996, ADV DIFFER EQUATIONS, V4, P689

[9] GENERALIZED HOPF-BIFURCATION AND ITS DUAL GENERALIZED HOMOCLINIC BIFURCATION [J].

JOYAL, P .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1988, 48 (03) :481-496

[10] Hilbert's 16th problem and bifurcations of planar polynomial vector fields [J].

Li, JB .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (01) :47-106

← 1 2 →