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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 038, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.038 (Mi sigma1019) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Joshua J. Capela, Jonathan M. Kressa, Sarah Postb

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
Full-text PDF (363 kB) Citations (19)
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DOI: https://doi.org/10.3842/SIGMA.2015.038
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.
Received: February 3, 2015; in final form April 21, 2015; Published online May 8, 2015
Bibliographic databases:
Document Type: Article
MSC: 33C45; 33D45; 33D80; 81R05; 81R12
Language: English
Citation: Joshua J. Capel, Jonathan M. Kress, Sarah Post, “Invariant Classification and Limits of Maximally Superintegrable Systems in 3D”, SIGMA, 11 (2015), 038, 17 pp.
Citation in format AMSBIB
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