Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Abstract

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.