On the study of limit cycles of a cubic polynomial system under \(\mathbb Z_{4}\)-equivariant quintic perturba\-tion
The authors study the number and distribution of limit cycles of a perturbed cubic Hamiltonian system which has 5 centers and 4 saddle points. The stability theory of singular points and singular close orbits are applied to study the Hopf, homoclinic loop and heteroclinic loop bifurcation of such system under \(\mathbb{Z}_4\)-equivariant quintic perturbation. By computing the Lyapunov constants, the authors find that the perturbed system has at least 16 limit cycles. Further, combining the Hopf bifurcation method and heteroclinic bifurcation method, the authors obtain at least 14 limit cycles.
scientific article; zbMATH DE number 2167912