Limit Cycle Bifurcations In A Class Of Quintic Z₂-equivariant Near-hamiltonian Systems

In this paper, we study a class of cubic Z₂-equivariant polynomial Hamiltonian systemsunder the perturbation of Z₂-equavariant polynomial of degree5. First, we consider theunperturbed system and obtain necessary and sufcient conditions for the critical point（0,1） to be a nilpotent saddle, center or cusp. We show that that it can have14diferentphase portraits. Using the methods of Hopf§Melnikov function and homoclinic bifurcationtheory, we study the bifurcation problem of the perturbed system and prove that thereexist12limit cycles.