Explicit metrics for a class of two-dimensional superintegrable systems
Mathematical Physics
2015-06-18 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are indeed globally defined on the two-sphere.
Cite
@article{arxiv.1403.0422,
title = {Explicit metrics for a class of two-dimensional superintegrable systems},
author = {Galliano Valent and Christian Duval and Vsevolod Shevchishin},
journal= {arXiv preprint arXiv:1403.0422},
year = {2015}
}
Comments
10 pages, no figure, to appear in the Proceedings of the Conference: "Finite dimensional integrable systems", 15th-19th of July 2013, CIRM, Luminy Campus, Marseille (France) published in the Journal of Geometry and Physics