On the number of limit cycles for some perturbed Hamiltonian polynomial systems (Q2720144)

Here, the authors consider perturbations of two Hamiltonian centers with two special Hamiltonians. First, they give the greatest number of isolated zeros (taking into account their multiplicity) of a class of Abelian integrals related to the corresponding perturbed Hamiltonian systems and consequently obtain the indicated number of limit cycles from the perturbations of the corresponding Hamiltonian center in the case of polynomial differential systems. Then, they give the relative cohomology decomposition of the corresponding polynomial one form and obtain an estimate number on the isolated zeros of the corresponding Abelian integral. They study also the problem of the maximum number of limit cycles surrounding a singular point in the perturbed system.