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Title: Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
Authors: Ballesteros, A.
Marrero, J.C.
Ravanpak, Z.
Issue Date: 2017
Description: Producción Científica
Citation: Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 145204 (25pp)
Abstract: Given a Lie-Poisson completely integrable bi-Hamiltonian system on R^n, we present a method which allows us to construct, under certain conditions, a completely integrable bi-Hamiltonian deformation of the initial Lie-Poisson system on a non-abelian Poisson-Lie group G_eta of dimension n, where eta \in R is the deformation parameter. Moreover, we show that from the two multiplicative (Poisson-Lie) Hamiltonian structures on G_eta that underly the dynamics of the deformed system and by making use of the group law on G_eta, one may obtain two completely integrable Hamiltonian systems on G_eta x G_eta. By construction, both systems admit reduction, via the multiplication in G_eta, to the deformed bi-Hamiltonian system in G_eta. The previous approach is applied to two relevant Lie-Poisson completely integrable bi-Hamiltonian systems: the Lorenz and Euler top systems.
Peer Review: SI
Language: eng
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:FM - Artículos de revista

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