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Levi-Civita regularization and geodesic flows for the `curved' Kepler problem
Leonor Garcia-Gutierrez, Mariano Santander
We introduce the regularization Levi-Civita parameter for the `curved Kepler', i.e., motion under the `Kepler-Coulomb' potential in a configuration space with any constant curvatur…
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
José F. Cariñena, Manuel F. Rañada, Mariano Santander
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are s…
(Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach
Francisco J. Herranz, Mariano Santander
A classical deformation procedure, based on universal enveloping algebras, Casimirs and curvatures of symmetrical homogeneous spaces, is applied to several cases of physical releva…
Two important examples of nonlinear oscillators
José F. Cariñena, Manuel F. Rañada, Mariano Santander
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scatteri…
A new Lie algebra expansion method: Galilei expansions to Poincare and Newton-Hooke
Francisco J. Herranz, Mariano Santander
We modify a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras so as to work for higher dimensions. This new improved and geometrical p…
The families of orthogonal, unitary and quaternionic unitary Cayley--Klein algebras and their central extensions
Francisco J. Herranz, Mariano Santander
The families of quasi-simple or Cayley--Klein algebras associated to antihermitian matrices over R, C and H are described in a unified framework. These three families include simpl…