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Proceedings Paper

Width of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation
Author(s): Stanislav M. Soskin; Oleg M. Yevtushenko; Riccardo Mannella
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Paper Abstract

We have found that the width of the chaotic layer in case of a low frequency of perturbation is significantly larger than that predicted by the conventional heuristic criteria. The underlying reason is a randomness of the sign of the energy change if the motion occurs in the vicinity of the separatrix, namely in the energy band of the order of the separatrix split. Moreover, in case when the separatrix is unbounded while the time-periodic perturbation is of a dipole type, we have found the dramatic widening of the chaotic layer as the perturbation frequency decreases. This occurs because the system in the slowly rocked Hamiltonian is accelerated during long periods of time and, therefore manages to gain large energy. The acceleration periods alternate with the braking ones so that the system returns to the vicinity of the separatrix where it may be trapped for some time in one of the regions of the phase space inside the separatrix loops. We have developed the explicit adiabatic theory which nicely agrees with simulations.

Paper Details

Date Published: 25 May 2004
PDF: 12 pages
Proc. SPIE 5471, Noise in Complex Systems and Stochastic Dynamics II, (25 May 2004); doi: 10.1117/12.546944
Show Author Affiliations
Stanislav M. Soskin, Institute of Semiconductor Physics (Ukraine)
Lancaster Univ. (United Kingdom)
Oleg M. Yevtushenko, Abdus Salam International Ctr. for Theoretical Physics (Italy)
Riccardo Mannella, Lancaster Univ. (United Kingdom)
Univ. di Pisa, INFM (Italy)

Published in SPIE Proceedings Vol. 5471:
Noise in Complex Systems and Stochastic Dynamics II
Zoltan Gingl, Editor(s)

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