摘要：This paper is devoted to study a center problem and a weak center problem for cubic systems in Z 4 -equivariant vector fields. By computing the Lyapunov constants and periodic constants carefully, we show that there exit five weak centers of second order, and center conditions and weak center conditions are given for this system. In terms of the problem of multiple weak centers, there are few results studied and thus our work is new and interesting. At the same time, we investigate the critical periodic bifurcation from a weak center.
关键词：Z 4 -equivariant ; Lyapunov constants ; center condition ; weak center
