Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers

被引：0
作者：
Weigu Li
Jaume Llibre
Jiazhong Yang
Zhifen Zhang
机构：
[1] Peking University,Department of Mathematics
[2] Universitat Autònoma de Barcelona,Departament de Matemàtiques
来源：
Journal of Dynamics and Differential Equations | 2009年 / 21卷
关键词：
Homogeneous centers; Quasi-homogeneous centers; Limit cycles; Primary 34C07; 34C08; 37G15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of any homogeneous and quasi-homogeneous center, which can be obtained using the Abelian integral method of first order. We show that these bounds are the best possible using the Abelian integral method of first order. We note that these centers are in general non-Hamiltonian. As a consequence of our study we provide the biggest known number of limit cycles surrounding a unique singular point in terms of the degree n of the system for arbitrary large n.
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页码：133 / 152
页数：19
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