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Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations

AutorBallesteros, A.; Marrero, J. C.; Ravanpak, Z.
Palabras claveLie–Poisson structures
Integrable deformations, coalgebras
Completely integrable systems
Bi-Hamiltonian systems
Hamiltonian systems
Poisson–Lie groups
Fecha de publicación10-mar-2017
EditorInstitute of Physics Publishing
CitaciónJournal of Physics A: Mathematical and Theoretical 50: 145204 (2017)
ResumenGiven a LiePoisson completely integrable bi-Hamiltonian system on ℝ, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial LiePoisson system on a non-abelian PoissonLie group G of dimension n, where n ∈ ℝ is the deformation parameter. Moreover, we show that from the two multiplicative (PoissonLie) Hamiltonian structures on G- that underly the dynamics of the deformed system and by making use of the group law on G, one may obtain two completely integrable Hamiltonian systems on G×G By construction, both systems admit reduction, via the multiplication in G, to the deformed bi-Hamiltonian system in G. The previous approach is applied to two relevant LiePoisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.
Descripción25 pags., 1 fig.
Versión del editorhttps://doi.org/10.1088/1751-8121/aa617b
URIhttp://hdl.handle.net/10261/163801
Identificadoresdoi: 10.1088/1751-8121/aa617b
issn: 1751-8121
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