Hamiltonian and quasi-Hamiltonian systems, Nambu-Poisson structures and symmetries

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

doi:10.1088/1751-8113/41/33/335209

Hamiltonian and quasi-Hamiltonian systems, Nambu-Poisson structures and symmetries

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

Mathematics

Universidad de Zaragoza

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The theory of Hamiltonian and quasi-Hamiltonian systems with respect to Nambu-Poisson structures is studied. It is proved that if a dynamical system is endowed with certain properties related to the theory of symmetries then it can be considered as a quasi-Hamiltonian (or Hamiltonian) system with respect to an appropriate Nambu-Poisson structure. Several examples of this construction are presented. These examples are related to integrability and also to superintegrability.

Original language	British English
Article number	335209
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	41
Issue number	33
DOIs	https://doi.org/10.1088/1751-8113/41/33/335209
State	Published - 22 Aug 2008

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AB - The theory of Hamiltonian and quasi-Hamiltonian systems with respect to Nambu-Poisson structures is studied. It is proved that if a dynamical system is endowed with certain properties related to the theory of symmetries then it can be considered as a quasi-Hamiltonian (or Hamiltonian) system with respect to an appropriate Nambu-Poisson structure. Several examples of this construction are presented. These examples are related to integrability and also to superintegrability.

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Hamiltonian and quasi-Hamiltonian systems, Nambu-Poisson structures and symmetries

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