What happens to an integrable system under a perturbation that destroys integrability? The KAM theorem (Kolmogorov, Arnold and Moser, 1954, 1960) says that for small perturbations, most tori about elliptic fixed points become slightly distorted but retain their topology. However, adjacent regions of phase space become chaotic, yielding regions on the SOS covered by seemingly random distributions of points. Within these chaotic regions, other nested elliptic fixed points and chaotic regions are found.
