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A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible.
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Kalnins E.G., Kress J.M., Miller, W.Jr. and Winternitz P., Superintegrable systems in Darboux spaces
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. III: 3D classical structure theory. J. Math. Phys
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. I: 2D classical structure theory. J. Math. Phys
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. II: The classical 2D Stäckel transform. J. Math. Phys
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Rañada M.F., Superintegrable n n =2 systems, quadratic constants of motion, and potentials of Drach. J. Math. Phys
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E. G. Kalnins, W. Miller, Jr. and G. S. Pogosyan. Completeness of multiseparable superintegrability in E 2 , C E_{2,C} . J. Phys. A: Math Gen
2000
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E. G. Kalnins, W. Miller Jr. and G. S. Pogosyan. Completeness of multiseparable superintegrability on the complex 2-sphere. J. Phys. A: Math Gen
2000
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Kalnins E.G., Kress J.M., Miller W.Jr. and Pogosyan G.S., Completeness of superintegrability in two-dimensional constant curvature spaces
2001
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Kalnins E.G., Kress J.MN., and Winternitz P., Superintegrability in a two-dimensional space of non-constant curvature
2002
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Kalnins E.G., Miller W.Jr., Williams G.C. and Pogosyan G.S., On superintegrable symmetry-breaking potentials in n n -dimensional Euclidean space. J. Phys. A: Math Gen
2002
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E.G.Kalnins, J.M.Kress, W.Miller Jr. and G.S.Pogosyan. Non degenerate superintegrable systems in n n dimensional complex Euclidean spaces. (To appear in Physics of Atomic Nuclei)
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J. T. Horwood, R. G. McLenaghan and R. G. Smirnov. Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space. Comm. Math. Phys
2005
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. V: 2D and 3D quantum systems. J. Math. Phys
2006
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Kalnins E.G., Kress J.M, and Miller W.Jr., Second order superintegrable systems in conformally flat spaces. IV: The classical 3D Stäckel transform and 3D classification theory. J. Math. Phys
2006
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C. Daskaloyannis and K Ypsilantis. Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold. J. Math. Phys
2006
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Kalnins E.G., Kress J.M, and Miller W.Jr., Fine structure for second order superintegrable systems (to appear in the procedings volumes of the IMA program on ”Symmetries and Overdetermined Systems of Partial Differential Equations.” ) 2007
2007
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