Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2009-06-18
Published in: "Hamitonian Chaos Beyond the KAM Theory", Eds.: A.C.J. Luo, V. Afraimovich; Nolinear Physical Science, Higher Ed
Nonlinear Sciences
Chaotic Dynamics
83 pages, review - submitted as a chapter for the book dedicated to George Zaslavsky; several figs. are of reduced quality, or
Scientific paper
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.
Khovanov I. A.
Mannella Riccardo
McClintock Peter V. E.
Soskin Marat S.
Yevtushenko O. M.
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