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MiS Preprint

Quasi-Hamiltonian Structure and Hojman Construction

José Cariñena, Partha Guha and Manuel Rañada


Given a smooth vector field $\Gamma$ and assuming the knowledge of an infinitesimal symmetry $X$, Hojman [J. Phys. A 29 (1996), no. 3, 667--674] proposed a method for finding both a Poisson tensor and a function $H$ such that $\Gamma$ is the corresponding Hamiltonian system.

In this paper we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [J.Math.Phys 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

Dec 5, 2006
Dec 5, 2006
MSC Codes:
37J35, 70H06
Poisson bivector, quasi Hamiltonian, KdV

Related publications

2007 Repository Open Access
José F. Carinena, Partha Guha and Manuel F. Ranada

Quasi-Hamiltonian structure and Hojman construction

In: Journal of mathematical analysis and applications, 332 (2007) 2, pp. 975-988