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Regular and Chaotic Dynamics

, Volume 15, Issue 6, pp 677–684 | Cite as

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

  • I. BasakEmail author
Research Articles

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.

Key words

integrable Hamiltonian sistems compatible Poisson structures bifurcations semisimple Lie algebras 

MSC2000 numbers

37K10 37J35 37J20 17B80 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Department de Matemàtica Aplicada IUniversitat Politecnica de CatalunyaBarcelonaSpain

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