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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 3, Pages 473–490 (Mi zvmmf170)  
This article is cited in 6 scientific papers (total in 6 papers)

The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations

R. I. Bogdanov, M. R. Bogdanov

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (2914 kB) Citations (6)
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Abstract: The weakly dissipative version of the Kolmogorov–Arnold–Moser theory deals with the dynamics of systems that are a weakly dissipative perturbation of Hamiltonian systems. In the framework of this approach, both regular (asymptotically stable (unstable) periodic motions) and stochastic (Arnold's web) dynamic properties are combined in the phase space. In this case, computer calculations are considerably simplified for the regular dynamics, which makes it possible to estimate physical parameters for stochastic components. A simple example of this approach is presented.
Key words: Bogdanov–Takens bifurcation, Bogdanov map, Euler scheme, adiabatic invariants, Arnold diffusion, treelike graph, hierarchical structure, periodic orbit.
Received: 09.07.2007
Revised: 27.08.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 3, Pages 447–463
DOI: https://doi.org/10.1007/s11470-008-3009-8
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: R. I. Bogdanov, M. R. Bogdanov, “The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 473–490; Comput. Math. Math. Phys., 48:3 (2008), 447–463
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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