Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Joshua J. Capel ; Jonathan M. Kress ; Sarah Post

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian manifolds can be obtained from singular limits of a generic system on the sphere. By using the invariant classification, the limits are geometrically motivated in terms of transformations of roots of the classifying polynomials.

Détail

Keywords: integrable systems; superintegrable systems; Lie algebra invariants; contractions.

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