Volume 15, Issue supplement 3, October 2008, Pages 43 - 52
Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces
- Angel Ballesteros, Alberto Enciso, Francisco José Herranz, Orlando Ragnisco
- Corresponding Author
- Angel Ballesteros
Available Online 1 October 2008.
- https://doi.org/10.2991/jnmp.2008.15.s3.5How to use a DOI?
- The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscilla- tor on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is pre- sented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superinte- grable anharmonic perturbations are explicitly constructed.
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Cite this article
TY - JOUR AU - Angel Ballesteros AU - Alberto Enciso AU - Francisco José Herranz AU - Orlando Ragnisco PY - 2008 DA - 2008/10 TI - Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces JO - Journal of Nonlinear Mathematical Physics SP - 43 EP - 52 VL - 15 IS - supplement 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2008.15.s3.5 DO - https://doi.org/10.2991/jnmp.2008.15.s3.5 ID - Ballesteros2008 ER -