The purpose of this article is the description of the classical dynamics of a resonant non-integrable Hamiltonian, which is written in the form

and where the term with behaves as a perturbation to the remaining integrable part (call it ) of the Hamiltonian. Apart from the chaotic region around the separatrix of , the dynamics of H is clearly different from that of only in the neighbourhood of low-order periodic orbits of , where coupling-induced resonance islands are seen to emerge. In order to model these resonance islands, is Taylor expanded in terms of its action integrals (thanks to recent exact analytical calculations) and the perturbation with is Fourier expanded in terms of the angles conjugate to the actions of . Retaining in the expansion only the term which is almost secular (because of the vicinity of the periodic orbit) leads to a local single resonance form of H. The classical frequencies and action integrals, which can be calculated analytically for this local expression of H, are shown to be in excellent agreement with `exact' numerical values deduced from power spectra and Poincaré surfaces of section. It is pointed out in the discussion that all the trajectories inside coupling-induced resonance islands share one almost degenerate classical frequency, and that the width of the coupling-induced island grows as the square root of the perturbation parameter , but is inversely proportional to the square root of the slow classical frequency at the periodic orbit and to the square root of the derivative, with respect to the first action integral, of the winding number.