On the number of limit cycles in double homoclinic bifurcations (Q1609568)

The authors consider perturbations of Hamiltonian systems in \(\mathbb{R}^2\). They assume that the unperturbed system possesses a double homoclinic loop (figure-eight-configuration) at a hyperbolic fixed point. The main results concern the maximal number of limit cycles near the given homoclinic orbits. The condition permitting the existence of the limit cycles are formulated in terms of Melnikov functions.