Invariant Classification and Limits of Maximally Superintegrable Systems in 3D

Symmetry Integrability and Geometry-Methods and Applications

article

Joshua J. Capel¹  Jonathan M. Kress¹  Sarah Post² 

[1] Department of Mathematics, University of New South Wales;Department of Mathematics, University of Hawai`i at Mānoa

关键词: integrable systems;    superintegrable systems;    Lie algebra invariants;    contractions;   

DOI  :  10.3842/SIGMA.2015.038

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown