On the number of limit cycles in quadratic perturbations of quadratic codimension-four centres

被引：22

作者：

Zhao, Yulin ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

NONLINEARITY | 2011年 / 24卷 / 09期

关键词：

HAMILTONIAN-SYSTEMS; PERIOD ANNULUS; CYCLICITY; BIFURCATIONS; SEGMENT; LOOPS;

D O I：

10.1088/0951-7715/24/9/007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of quadratic codimension-four centres Q(4). Gavrilov and Iliev set an upper bound of eight for the number of limit cycles produced from the period annuli around the centre. Based on Gavrilov-Iliev's proof, we prove in this paper that the perturbed system has at most five limit cycles which emerge from the period annuli around the centre. We also show that there exists a perturbed system with three limit cycles produced by the period annuli of Q(4).

引用

页码：2505 / 2522

页数：18

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