Drastic facilitation of the onset of global chaos due to an extremum in the dependence of eigenfrequency on energy

摘要

The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic perturbation, the onset of global chaos may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. One of the most important manifestations of this effect is a drastic increase of the energy range involved into the unbounded chaotic transport in spatially periodic system driven by a rather weak time-periodic force, which results in turn in the drastic increase either of the dc conductivity, if the system caries an electric charge, or of the escape rate, if the system is subject to noise. We develop the asymptotic theory and verify it in simulations. Various generalizations are delineated, in particular for the case of a time-independent perturbation.