Large excursions of action within the resonance of a degenerate Hamiltonian system with two degrees of freedom

Abstract

We investigate the width of the resonance zone in a degenerate Hamiltonian system with two degrees of freedom, in which the Hamiltonian lacks the quadratic term in the Taylor expansion. This leads to larger excursions of action in the phase space than the nondegenerate one, and corresponding resonance frequency widths would become narrower. However, in contrast to the nonautonomous Hamiltonian system with one and half degree of freedom, we find that the above case is not generic and only occurs at particular resonances. An example relevant to the interaction of resonances is considered. Analytic results are verified in numerical simulations.