Comments on Stable Motions in Nonlinear Coupled Resonances

It is shown that, of all nonlinear coupled resonances of the form m V1+ n V2 = k where m, n and k are positive integers and m + n ?? 3, those with m or n = 1 exhibit a different property compared to others in their stable regions of phase space. The difference explains the paradoxical result obtained by Sturrock and Guignard that there are points of arbitrarily small amplitudes which lie outside the stable region.