RT info:eu-repo/semantics/article
T1 A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)
A1 Ballesteros Castañeda, Ángel
A1 Campoamor Stursberg, Rutwig
A1 Fernandez Saiz, Eduardo
A1 Herranz, F.J.
A1 Lucas Veguillas, Javier de
AB Based on a recently developed procedure to construct Poisson-Hopf deformations of Lie–Hamilton systems, a novel unified approach to nonequivalent deformations of Lie–Hamilton systems on the real plane with a Vessiot–Guldberg Lie algebra isomorphic to sl(2) is proposed. This, in particular, allows us to define a notion of Poisson–Hopf systems in dependence of aparameterized family of Poisson algebra representations. Such an approach is explicitly illustrated by applying it to the three non-diffeomorphic classes of sl(2) Lie–Hamilton systems. Our results cover deformations of the Ermakov system, Milne–Pinney, Kummer–Schwarz and several Riccati equations as well as of the harmonic oscillator (all of them with t-dependent coefficients). Furthermore t-independent constants of motion are given as well. Our methods can be employed to generate other Lie–Hamilton systems and their deformations for other Vessiot–Guldberg Lie algebras and their deformations.
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/33632
UL http://uvadoc.uva.es/handle/10324/33632
LA eng
NO Dobrev, V. (ed.). Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, 2018. p. 347-366
NO Producción Científica
DS UVaDOC
RD 30-jun-2024