On the number of limit cycles bifurcating from a non-global degenerated center (Q868780)

The authors give an upper bound for the number of zeros of an Abelian integral which controls the number of limit cycles bifurcating from the periodic orbits of an integrable system with a quasi-homogeneous Hamiltonian. The tools used in their proofs are the argument principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis.