  The Melnikov method is applied to periodically perturbed open systems modeled
by an inverse--square--law attraction center plus a quadrupolelike term. A
compactification approach that regularizes periodic orbits at infinity is
introduced. The (modified) Smale-Birkhoff homoclinic theorem is used to study
transversal homoclinic intersections. A larger class of open systems with
degenerated (nonhyperbolic) unstable periodic orbits after regularization is
also briefly considered.
