Not sure if this question belongs in physics or mathematics.
Recently I have been making some computer simulations of somebody swinging on a playground swing at varying frequencies. Specifically I was interested if it is possible to cause a 1:3 resonance by moving the swinging person's centre of mass three times as fast as the frequency of the swing. By KAM theory I would expect that this should be the case.
However, when I did the computation swinging at 1:3 (or at any other rational multiple except 1:2) did not cause any resonances.
Typically KAM theory only tells you something about the stable solutions and not the resonant ones. So it is not really a contradiction. However I still would except that you can cause resonance at 1:3. Or would this resonance only be visible at very large time scales?