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A new approach to the treatment of separatrix chaos and its applications.

Research output: Contribution in Book/Report/ProceedingsChapter

Published

Publication date2010
Host publicationHamiltonian Chaos Beyond the KAM Theory
EditorsA. C. J. Luo, V. Afraimovich
Place of publicationBeijng and Heidelberg
PublisherHigher Education Press and Springer
Pages51-141
Number of pages91
ISBN (Print)978-3-642-12717-5
Original languageEnglish

Publication series

NameNonlinear Physical Science
PublisherHigher Education Press and Springer

Abstract

We consider time-periodically perturbed ID 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.