Bi-Hamiltonian systems of deformation type |
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| Institution: | 1. Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, Torino 10149, Italy;2. Dipartimento di Matematica “Felice Casorati”, Università degli Studi di Pavia, Via Adolfo Ferrata 5, Pavia 27100, Italy;3. Département d’Opérations et Systèmes de Décision, Université Laval, Pavillon Palasis-Prince, 2325, rue de la Terrasse, Québec, QC G1V 0A6, Canada;4. Dipartimento di Matematica ed Informatica, Università degli Studi di Cagliari, Palazzo delle Scienze, Via Ospedale 72, Cagliari 09124, Italy;5. Department of Operations, Energy, and Environmental Management, University of Klagenfurt, Universität Straße 65-67, Klagenfurt 9020, Austria;1. Dipartimento di Matematica “Felice Casorati”, Università degli Studi di Pavia, via Adolfo Ferrata 5, I-27100, Pavia, Italy;2. Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, I-10149, Torino (Italy) |
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| Abstract: | In this paper, after some recalls about Poisson cohomology, we first study what the general method is in order to obtain a bi-Hamiltonian formulation of a given Hamiltonian system by means of a deformation. Then we show that the bi-Hamiltonian formulation which results from the deformation of a Poisson structure by means of a suitable non-Noether symmetry cannot explain the complete integrability for a large class of Arnold–Liouville integrable systems; next we prove that the deformation must be made in this context by a suitable mastersymmetry. At last, we give several examples. |
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