Chaos in the 3 : 1 mean-motion resonance revisited

Numerical simulations of orbits in the 3 : 1 mean-motion resonance reveal the existence of nearly closed homoclinic loops attached to a periodic orbit. Chaos in the vicinity of these loops is associated not with the separatrix of libration as in Wisdoms study but with secular instabilities first noted by Henrard and Caranicolas.