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oai:uvadoc.uva.es:10324/408472025-02-24T09:32:06Zcom_10324_22154com_10324_954com_10324_894col_10324_22155

Ballesteros Castañeda, Ángel Campoamor Stursberg, Rutwig Fernandez Saiz, Eduardo Herranz, Francisco J. Lucas Veguillas, Javier de 2020-05-16T10:01:34Z 2020-05-16T10:01:34Z 2018 Journal of Physics A: Mathematical and Theoretical, 2018, vol. 51, 065202 1751-8121 http://uvadoc.uva.es/handle/10324/40847 10.1088/1751-8121/aaa090 Journal of Physics A: Mathematical and Theoretical 51 Hopf algebra deformations are merged with a class of Lie systems of Hamiltonian type, the so-called Lie–Hamilton systems, to devise a novel formalism: the Poisson–Hopf algebra deformations of Lie–Hamilton systems. This approach applies to any Hopf algebra deformation of any Lie–Hamilton system. Remarkably, a Hopf algebra deformation transforms a Lie–Hamilton system, whose dynamic is governed by a finite-dimensional Lie algebra of functions, into a non-Lie–Hamilton system associated with a Poisson–Hopf algebra of functions that allows for the explicit description of its t-independent constants of the motion from deformed Casimir functions. We illustrate our approach by considering the Poisson–Hopf algebra analogue of the nonstandard quantum deformation of sl(2) and its applications to deform wellknown Lie–Hamilton systems describing oscillator systems, Milne–Pinney equations, and several types of Riccati equations. In particular, we obtain a new position-dependent mass oscillator system with a time-dependent frequency. eng info:eu-repo/semantics/openAccess © 2018 IOP Publishing Ltd Poisson-Hopf algebra deformations of Lie-Hamilton systems info:eu-repo/semantics/article