Stochasticity and reconnection in Hamiltonian systems

A general class of Hamiltonian systems is studied in which neighboring phase-space islands are shifted in phase. This leads to reconnection of Kolmogorov-Arnold-Moser level curves and necessitates a reexamination of the island overlap criterion for the breakdown of adiabatic barriers between island chains. An analytic reconnection threshold is derived from an averaged Hamiltonian and found to agree closely with numerical surfaces of section for a model mapping. Numerous applications to physical problems are indicated.