Abstract
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.
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Meletlidou, E., Stagika, G. & Ichtiaroglou, S. Non-Integrability and Structure of the Resonance Zones in a Class of Galactic Potentials. Celestial Mech Dyn Astr 91, 323–335 (2005). https://doi.org/10.1007/s10569-004-4494-2
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DOI: https://doi.org/10.1007/s10569-004-4494-2