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Regul. Chaotic Dyn., 2010, Volume 15, Issue 4-5, Pages 431–439 (Mi rcd508)  

On the 60th birthday of professor V.V. Kozlov

Criteria for existence of a Hamiltonian structure

O. I. Bogoyavlenskij, A. P. Reynolds

Department of Mathematics, Queen's University, Kingston, K7L 3N6, Canada

Abstract: The necessary and sufficient conditions are derived for the existence of a Hamiltonian structure for 3-component non-diagonalizable systems of hydrodynamic type. The conditions are formulated in terms of tensor invariants defined by the metric $h_{ij}(u)$ constructed from the Haantjes (1,2)-tensor.

Keywords: Poisson brackets, conformally flat metric, covariant derivatives, Weyl–Schouten equations, Haantjes tensor

DOI: https://doi.org/10.1134/S1560354710040039


Bibliographic databases:

MSC: 35L60
Received: 01.10.2009
Accepted:10.10.2009
Language:

Citation: O. I. Bogoyavlenskij, A. P. Reynolds, “Criteria for existence of a Hamiltonian structure”, Regul. Chaotic Dyn., 15:4-5 (2010), 431–439

Citation in format AMSBIB
\Bibitem{BogRey10}
\by O. I. Bogoyavlenskij, A. P. Reynolds
\paper Criteria for existence of a Hamiltonian structure
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 4-5
\pages 431--439
\mathnet{http://mi.mathnet.ru/rcd508}
\crossref{https://doi.org/10.1134/S1560354710040039}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2679757}
\zmath{https://zbmath.org/?q=an:1252.35187}


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