Figure 4

(a) The radial family of periodic orbits of the integrable limit (\(\epsilon =0\)) of system (7) in toroidal coordinates. (b) The tangential family of periodic orbits of the same system. This family is destroyed for \(\epsilon >0\). (c) Taking the intersection at \(\theta _2=0\) for the integrable system (\(\epsilon =0\)) shows the quasiperiodic tori as concentric circles. The three enlarged light green points correspond to one of the periodic orbits on a resonant torus. (d) Under the non-integrable perturbation (\(\epsilon =10^{-3}\)), most quasiperiodic tori persist (dark blue, dark red), but the resonant torus is destroyed and replaced by a spectral gap with pendulum-type dynamics (green, red, blue). The light green points survive as an elliptic periodic orbit.