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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 6, Pages 677–684
DOI: https://doi.org/10.1134/S1560354710060043 (Mi rcd527) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Bifurcation analysis of the Zhukovskii–Volterra system via bi-Hamiltonian approach

I. Basak

Department de Matemàtica Aplicada I, Universitat Politecnica de Catalunya, Barcelona, E-08028 Spain
Citations (1)
DOI: https://doi.org/10.1134/S1560354710060043
Abstract: The main goal of this paper consists of bifurcation analysis of classical integrable Zhukovskii–Volterra system. We use the fact that the ZV system is bi-Hamiltonian and apply new techniques [1] for analysis of singularities of bi-Hamiltonian systems, which can be formulated as follows: the structure of singularities of a bi-Hamiltonian system is determined by that of the corresponding compatible Poisson brackets.
Keywords: integrable Hamiltonian sistems, compatible Poisson structures, bifurcations, semisimple Lie algebras.
Received: 28.12.2009
Accepted: 23.02.2010
Bibliographic databases:
Document Type: Article
MSC: 37K10, 37J35, 37J20, 17B80
Language: English
Citation: I. Basak, “Bifurcation analysis of the Zhukovskii–Volterra system via bi-Hamiltonian approach”, Regul. Chaotic Dyn., 15:6 (2010), 677–684
Citation in format AMSBIB
\Bibitem{Bas10}
\by I. Basak
\paper Bifurcation analysis of the Zhukovskii–Volterra system via bi-Hamiltonian approach
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 6
\pages 677--684
\mathnet{http://mi.mathnet.ru/rcd527}
\crossref{https://doi.org/10.1134/S1560354710060043}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2747178}
\zmath{https://zbmath.org/?q=an:1209.37072}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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