MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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