Complete study on a bi-center problem for the Z 2-equivariant cubic vector fields

被引：23
作者：
Liu, Yi Rong [1 ]
Li, Ji Bin [1 ,2 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
[2] Kunming Univ Sci & Technol, Sch Sci, Kunming 650093, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Center problem; Liapunov constant; focal value; integral factor; invariant integral; cubic polynomial system; LIMIT-CYCLES; PLANAR SYSTEM; EQUATIONS;
D O I：
10.1007/s10114-011-8412-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the planar Z (2)-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z (2)-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme aOE (c) 6 a 6 > is proved.
引用
收藏
页码：1379 / 1394
页数：16
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