On the Limit Cycles Bifurcating from a Quadratic Reversible Center of Genus One

被引：3

作者：

Peng, Linping ^{[1
]}

Li, You ^{[1
]}

机构：

[1] Beihang Univ, Sch Math & Syst Sci, LIMB, Minist Educ, Beijing 100191, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2014年 / 11卷 / 02期

关键词：

Quadratic reversible system; genus one; period annulus; bifurcation of limit cycles; Abelian integral; UNBOUNDED HETEROCLINIC LOOPS; HAMILTONIAN-SYSTEMS; PERIOD ANNULI; INTEGRABLE SYSTEM; HOMOCLINIC LOOP; HILBERT PROBLEM; PERTURBATIONS; CYCLICITY; N=2;

D O I：

10.1007/s00009-013-0325-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is concerned with the bifurcation of limit cycles in perturbations of a quadratic reversible system with a center of genus one. By studying the properties of the auxiliary curve and centroid curve defined by the Abelian integrals, we have proved that under small quadratic perturbations, at most two limit cycles arise from the period annulus surrounding the quadratic reversible center, and the bound is sharp. This partially verifies Conjecture 1 given in Gautier et al. (Discrete Contin Dyn Syst 25:511-535, 2009).

引用

页码：373 / 392

页数：20

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