Quasi-Hamiltonian Structure and Hojman Construction

José Cariñena, Partha Guha, and Manuel Rañada

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Submission date: 05. Dec. 2006
Pages: 18
published in: Journal of mathematical analysis and applications, 332 (2007) 2, p. 975-988 
DOI number (of the published article): 10.1016/j.jmaa.2006.08.092
Bibtex
MSC-Numbers: 37J35, 70H06
Keywords and phrases: Poisson bivector, quasi Hamiltonian, KdV
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Abstract:
Given a smooth vector field

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 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.