Soskin, S. M., Mannella, R., Yevtushenko, O. M., Khovanov, Igor and McClintock, P. V. E. (2010) A new approach to the treatment of Separatrix Chaos and its applications. In: Hamitonian chaos beyond the KAM theory: dedicated to George M. Zaslavsky (1935—2008). Nonlinear physical science . New York: Springer. ISBN 9783642127175

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Abstract

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.

Item Type:	Book Item
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Chaotic behavior in systems, Hamiltonian systems -- Research, Differentiable dynamical systems, Stochastic systems
Series Name:	Nonlinear physical science
Publisher:	Springer
Place of Publication:	New York
ISBN:	9783642127175
Book Title:	Hamitonian chaos beyond the KAM theory: dedicated to George M. Zaslavsky (1935—2008)
Date:	August 2010
Number of Pages:	36
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
Description:	This version of the chapter represents just about 1/3 of the text in order to accord the copyright of the publisher. The presented parts are in bold in the contents.
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URI:	http://wrap.warwick.ac.uk/id/eprint/3312

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