Bifurcations of limit cycles in equivariant quintic planar vector fields

In this paper, we obtain 23 limit cycles for a Z3-equivariant near-Hamiltonian system of degree 5 which is the perturbation of a Z6-equivariant quintic Hamiltonian system. The configuration of these limit cycles is new and different from the configuration obtained by H.S.Y. Chan, K.W. Chung and J. Li, where the unperturbed system is a Z3-equivariant quintic Hamiltonian system. Our unperturbed system is different from the unperturbed systems studied by Y. Wu and M. Han. The limit cycles are obtained by Poincaré-Pontryagin theorem and Poincaré-Bendixson theorem.