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- W3121293341 abstract "A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the Hamiltonian and its integrals of motion are given in a linear ambient space $R^{N+1}$, and secondly they are expressed in terms of two geodesic coordinate systems on the ND spaces themselves, with an explicit dependence on the curvature as a parameter. On the sphere, the potential is interpreted as a superposition of N+1 oscillators. Furthermore each Lie algebra generator provides an integral of motion and a set of 2N-1 functionally independent ones are explicitly given. In this way the maximal superintegrability of the ND Euclidean Smorodinsky-Winternitz system is shown for any value of the curvature." @default.
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- W3121293341 date "2003-02-05" @default.
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- W3121293341 title "Maximal superintegrability on<i>N</i>-dimensional curved spaces" @default.
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- W3121293341 doi "https://doi.org/10.1088/0305-4470/36/7/101" @default.
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