Z_2-Equivariant Cubic System Which Yields 13 Limit Cycles  

作　　者：Yi-rong LIU Ji-bin LI 

机构地区：[1]School of Mathematics,Central South University [2]Department of Mathematics,Zhejiang Normal University [3]School of Science,Kunming University of Science and Technology

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第3期781-800,共20页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11371373 and 10831003)

摘　　要：For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.

关 键 词：planar dynamical system limit cycles BIFURCATIONS Lyapnov constant weak focus 

分 类 号：O175[理学—数学]