RT info:eu-repo/semantics/article
T1 Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
A1 Ballesteros Castañeda, Ángel
A1 Marrero, Juan C.
A1 Ravanpak, Zohreh
AB 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 showthat from the two multiplicative (Poisson-Lie) Hamiltonian structures on G_eta that underly thedynamics 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 integrablebi-Hamiltonian systems: the Lorenz and Euler top systems.
YR 2017
FD 2017
LK http://uvadoc.uva.es/handle/10324/33635
UL http://uvadoc.uva.es/handle/10324/33635
LA eng
NO Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 145204 (25pp)
NO Producción Científica
DS UVaDOC
RD 18-may-2024