73 citations · 2.5k across the 138 of their papers we have counts for
59 papers · 1 filter
Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations
Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz
Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that enlarge a recently proposed SIS epidemic model with a variable infection rate a…
A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated cois…
Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system
Alfonso Blasco, Ivan Gutierrez-Sagredo, Francisco J. Herranz
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by where …
Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The complete classification of classical -matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum…
Poisson-Hopf deformations of Lie-Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
The formalism for Poisson-Hopf (PH) deformations of Lie-Hamilton systems is refined in one of its crucial points concerning applications, namely the obtention of effective and comp…
The -(A)dS noncommutative spacetime
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The (3+1)-dimensional -(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the -(A)dS Poisson homogeneous space. Th…
Curvature as an integrable deformation
Angel Ballesteros, Alfonso Blasco, Francisco J. Herranz
The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability prop…
Cayley-Klein Poisson homogeneous spaces
Francisco J. Herranz, Angel Ballesteros, Ivan Gutierrez-Sagredo +1
The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogene…
Drinfel'd double structures for Poincaré and Euclidean groups
Ivan Gutierrez-Sagredo, Angel Ballesteros, Francisco J. Herranz
All non-isomorphic three-dimensional Poisson homogeneous Euclidean spaces are constructed and analyzed, based on the classification of coboundary Lie bialgebra structures of the Eu…
The Poincaré group as a Drinfel'd double
Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz
The eight nonisomorphic Drinfel'd double (DD) structures for the Poincaré Lie group in (2+1) dimensions are explicitly constructed in the kinematical basis. Also, the two existing…
A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
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 syste…
Poisson-Hopf algebra deformations of Lie-Hamilton systems
Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz +2
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 defo…
Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
Jose F. Cariñena, Francisco J. Herranz, Manuel F. Rañada
The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian into a geodesic Hamiltonian with one additional degree of freedom, is applie…
Lie-Hamilton systems on curved spaces: A geometrical approach
Francisco J. Herranz, Javier de Lucas, Mariusz Tobolski
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a -dependent vector field taking values in a fin…
Factorization approach to superintegrable systems: Formalism and applications
Angel Ballesteros, Francisco J. Herranz, Sengul Kuru +1
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, th…
The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +3
In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system wh…
An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +2
In this paper we quantize the -dimensional classical Hamiltonian system , that can be regarded as a deformation of the Coulomb prob…
Lie symmetries for Lie systems: applications to systems of ODEs and PDEs
P. G. Estévez, F. J. Herranz, J. de Lucas +1
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a g…
Twisted (2+1) -AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
Ángel Ballesteros, Francisco J. Herranz, Catherine Meusburger +1
We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of…
A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
Angel Ballesteros, Francisco J. Herranz, Catherine Meusburger
We show that the Drinfel'd double associated to the standard quantum deformation is isomorphic to the (2+1)-dimensional AdS algebra with the initial deformation paramet…
Lie-Hamilton systems on the plane: properties, classification and applications
A. Ballesteros, A. Blasco, F. J. Herranz +2
We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a -dependent vector field taking values in a fin…
A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system
Angel Ballesteros, Alberto Enciso, Francisco J. Herranz +2
The -dimensional quantum Hamiltonian is shown to be exa…
From constants of motion to superposition rules for Lie-Hamilton systems
A. Ballesteros, J. F. Cariñena, F. J. Herranz +2
A Lie system is a nonautonomous system of first-order differential equations possessing a superposition rule, i.e. a map expressing its general solution in terms of a generic finit…
Drinfel'd doubles for (2+1)-gravity
Angel Ballesteros, Francisco J. Herranz, Catherine Meusburger
All possible Drinfel'd double structures for the anti-de Sitter Lie algebra so(2,2) and de Sitter Lie algebra so(3,1) in (2+1)-dimensions are explicitly constructed and analysed in…