Quasi-Hamiltonian structure and Hojman construction

José F. Cariñena, Partha Guha, Manuel F. Rañada

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Given a smooth vector field Γ and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that Γ 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 [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

Original languageBritish English
Pages (from-to)975-988
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Aug 2007


  • KdV
  • Poisson bivector
  • Quasi-Hamiltonian


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