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Oleg Bogoyavlenskij

ul. Gubkina 8, Moscow, 119991, Russia
Kingston, K7L 3N6, Canada
V.A. Steklov Institute of Mathematics, Russian Academy of Sciences
Department of Mathematics, Queen’s University


Bogoyavlenskij O. I., Reynolds A. P.
Criteria for existence of a Hamiltonian structure
2010, vol. 15, no. 4-5, pp.  431-439
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
Citation: Bogoyavlenskij O. I., Reynolds A. P.,  Criteria for existence of a Hamiltonian structure, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 431-439
Bogoyavlenskij O. I.
Integrable Lotka–Volterra systems
2008, vol. 13, no. 6, pp.  543-556
Infinite- and finite-dimensional lattices of Lotka–Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka–Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.
Keywords: Lax representation, Hamiltonian structures, Casimir functions, Riemannian surfaces, Lotka–Volterra systems, integrable lattices
Citation: Bogoyavlenskij O. I.,  Integrable Lotka–Volterra systems, Regular and Chaotic Dynamics, 2008, vol. 13, no. 6, pp. 543-556

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