For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary 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 Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary 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 Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
