Maslov indices of resonant tori

It is well known that the resonant tori of an integrable, classical Hamiltonian system break up under a small perturbation into new tori which wind around the remaining nonresonant tori. It turns out that the Maslov indices of one of these satellite tori depend on the Maslov indices of its unperturbed, resonant parent, and on the integers which enter into the resonance condition. They do not, however, depend on the functional form of the Hamiltonian or the perturbation. Our results are valid for any number of degrees of freedom.