Joshua J. Capel, Jonathan M. Kress, Sarah Post, “Invariant Classification and Limits of Maximally Superintegrable Systems in 3D”, SIGMA, 2015, Volume 11,038, 17 pp.

This article is cited in 20 papers

Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Joshua J. Capel^a, Jonathan M. Kress^a, Sarah Post^b

^a Department of Mathematics, University of New South Wales, Sydney, Australia
^b Department of Mathematics, University of Hawai'i at Mānoa, Honolulu, HI, 96822, USA

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.

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

MSC: 33C45; 33D45; 33D80; 81R05; 81R12

Received: February 3, 2015; in final form April 21, 2015; Published online May 8, 2015

Language: English

DOI: 10.3842/SIGMA.2015.038