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

摘要

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