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

Stanislav M. Soskin; Oleg M. Yevtushenko; Riccardo Mannella

doi:10.1117/12.546938

25 May 2004 Theory for the drastic facilitation of the onset of global chaos between separatrices of a Hamilton system

Stanislav M. Soskin, Oleg M. Yevtushenko, Riccardo Mannella

Author Affiliations +

Proceedings Volume 5471, Noise in Complex Systems and Stochastic Dynamics II; (2004) https://doi.org/10.1117/12.546938
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain

Abstract

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.

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Stanislav M. Soskin, Oleg M. Yevtushenko, and Riccardo Mannella "Theory for the drastic facilitation of the onset of global chaos between separatrices of a Hamilton system", Proc. SPIE 5471, Noise in Complex Systems and Stochastic Dynamics II, (25 May 2004); https://doi.org/10.1117/12.546938

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