Non-Integrability and Structure of the Resonance Zones in a Class of Galactic Potentials

The structure of the resonance zone in nearly integrable Hamiltonian systems is studied by a more general method than the pendulum approximation. This method applies to the case of a non-degenerate integrable part in the Hamiltonian. This problem may be overcome in a class of galactic-type polynomial potentials, in the case where the higher-order term is by itself integrable. An illustrative example is worked out.