|Title: ||Poisson-Hopf algebra deformations of Lie-Hamilton systems|
|Authors: ||Ballesteros, A.|
de Lucas, J.
|Issue Date: ||2018|
|Citation: ||Journal of Physics A: Mathematical and Theoretical, vol. 51 (2018) 065202|
|Abstract: ||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 non-standard quantum deformation of sl(2) and its applications to deform well-known 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.|
|Peer Review: ||SI|
|Appears in Collections:||FM - Artículos de revista|
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