A new approach to the treatment of Separatrix Chaos and its applications
Soskin, S. M., Mannella, R., Yevtushenko, O. M., Khovanov, I. A. 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
WRAP_Khovanov_Chapter_ZaslavskyBook.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://springer.com/978-3-642-12717-5
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|
|Place of Publication:||New York|
|Book Title:||Hamitonian chaos beyond the KAM theory: dedicated to George M. Zaslavsky (1935—2008)|
|Official Date:||August 2010|
|Number of Pages:||36|
|Access rights to Published version:||Restricted or Subscription Access|
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.
1. Abdullaev S.S.: Construction of Mappings for Hamiltonian Systems and Their Applications.
Actions (login required)