We classify the Hamiltonians H=px2+ py2 +V(x,y) of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H=J12+J22+ J32+V(x,y,z) on the complex 2-sphere where x2+y2+z2=1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.
Institute for Mathematics and Its Applications>IMA Preprints Series
Kalnins, E.G.; Kress, J.M.; Pogosyan, G.; Miller, Jr., W..
Completeness of superintegrability in two dimensional constant curvature spaces.
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