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Drastic facilitation of the onset of global chaos in a periodically driven Hamiltonian system due to an extremum in the dependence of eigenfrequency on energy

Soskin, S. M. and Yevtushenko, O. M. and Mannella, R. (2003) Drastic facilitation of the onset of global chaos in a periodically driven Hamiltonian system due to an extremum in the dependence of eigenfrequency on energy. Physical review letters, 90 . p. 174101. ISSN 0031-9007

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Abstract

SUMMARY 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 {\it 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 {\it weak} time-periodic force, provided the driving frequency approaches the extremal eigenfrequency or its harmonics. We develop the asymptotic theory and verify it in simulations.

Item Type: Article
Additional Information: Imported from arXiv
Subjects: Area02 - Scienze fisiche > FIS/03 - Fisica della materia
Divisions: Dipartimenti (from 2013) > DIPARTIMENTO DI FISICA
Depositing User: dott.ssa Sandra Faita
Date Deposited: 06 Aug 2013 13:36
Last Modified: 06 Aug 2013 13:36
URI: http://eprints.adm.unipi.it/id/eprint/1428

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