Resonant islands without separatrix chaos

Abstract

An alternative type of Hamiltonian nonlinear resonant island is analyzed. In the usual case where the resonant island is pendulumlike, chains bifurcated out of the central elliptic point undergo infinite cascades of period-doubling bifurcations as they approach the island boundary. In the present case we find that those chains undergo either period doubling or inverse saddle-node bifurcations, depending on the strength of perturbing terms. In the saddle-node case we show that just after a reconnection process, external chains cross the island boundary to collapse against the bifurcated internal chains.