Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold

Abstract

In this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of superintegrable systems. Analytic formulas for the involved integrals are calculated in all the cases. All the known superintegrable systems are classified as special cases of these six general classes.

LaTeX, 72 pages. Extended version of the published version in JMP

References in corpus (5)

• Completeness of superintegrability in two-dimensional constant curvature spaces
• Superintegrability with third order invariants in quantum and classical mechanics
• Superintegrable Systems in Darboux spaces
• Superintegrability in a two-dimensional space of non-constant curvature
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion

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