Width of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation

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

doi:10.1117/12.546944

25 May 2004 Width of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation

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/10.1117/12.546944
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain

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.

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Stanislav M. Soskin, Oleg M. Yevtushenko, and Riccardo Mannella "Width of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation", Proc. SPIE 5471, Noise in Complex Systems and Stochastic Dynamics II, (25 May 2004); https://doi.org/10.1117/12.546944

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KEYWORDS

Chaos

Complex systems

Solids

Computer simulations

Modulation

Physics

Estimation theory

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