Explicit metrics for a class of two-dimensional cubically superintegrable systems

Galliano Valent (1) , Christian Duval (2, 3) , Vsevolod Shevchishin (4)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E2 Géométrie, Physique et Symétries
4 HSE - Faculty of Mathematics, National Research University Higher School of Economics

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.

Mots clés: cubic integrals; global topology; Superintegrable systems

Domaines: Physique mathématique [math-ph]

Galliano Valent, Christian Duval, Vsevolod Shevchishin. Explicit metrics for a class of two-dimensional cubically superintegrable systems. Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics, Jul 2013, Marseille, France. pp.354-372, ⟨10.1016/j.geomphys.2014.08.004⟩. ⟨hal-01259070⟩