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Title: A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)
Authors: Ballesteros, A.
Campoamor-Stursberg, R.
Fernandez-Saiz, E.
Herranz, F.J.
de Lucas, J.
Issue Date: 2018
Citation: Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, V. Dobrev (ed.), (2018) 347-366
Abstract: 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 a parameterized 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.
Peer Review: SI
Language: eng
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:FM - Artículos de revista

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