Regular and Chaotic Dynamics

, Volume 15, Issue 4–5, pp 431–439 | Cite as

Criteria for existence of a Hamiltonian structure

  • O. I. BogoyavlenskijEmail author
  • A. P. Reynolds
Special Issue: Valery Vasilievich Kozlov-60


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.

Key words

Poisson brackets conformally flat metric covariant derivatives Weyl-Schouten equations Haantjes tensor 

MSC2000 numbers



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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada

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