Quasi-Hamiltonian Structure and Hojman Construction
José Cari\ nena, Partha Guha, and Manuel Ra\ nada
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Submission date: 05. Dec. 2006
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
MSC-Numbers: 37J35, 70H06
Keywords and phrases: Poisson bivector, quasi Hamiltonian, KdV
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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
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.