On the limit cycles of a Hamiltonian under Z4-equivariant quintic perturbation

Abstract

Abstract The number and distribution of limit cycles of a perturbed Z 4 -equivariant Hamiltonian system are studied in this paper. The existence theory and stability theory of singular close orbits are applied to study the given perturbed system. By using the small parametric perturbation skills of differential equations, we find that the perturbed Z 4 -equivariant system has at least 20 limit cycles. The distribution of the above 20 limit cycles is also given.