Phase-space representation of the divergent resonant encounter. Prior to the encounter, the system resides on the stable equilibrium point in the vicinity of the origin. At the time of the encounter, the stable equilibrium point and the unstable equilibrium point (on which the separatrix resides) join and the system obtains a circulational trajectory, related to the separatrix. As the system marches further away from resonance, the circulating trajectory asymptotically approaches a circle, while conserving the encapsulated area, .