Theory for the drastic facilitation of the onset of global chaos between separatrices of a Hamiltonian system

We present a heuristic theory describing the recently discovered (PRL 90, 17410 (2003)) drastic facilitation of the onset of global chaos in time periodically perturbed Hamiltonian systems possessing two or more separatrices: the minimal magnitude of the perturbation which provides chaos in the whole energy range between the separatrices possesses deep spikes as a function of the perturbation frequency. 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 the separatrices. We discuss a few applications: the increase of the dc conductivity of the 2D electron gas in a magnetic superlattice, the decrease of the activation barrier in the problem of noise-induced escape, the facilitation of the stochastic web formation in time periodically perturbed oscillators.