Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

Details Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

2006-10-17

arxiv.org/abs/math-ph/0610040v1

J.Phys.A40:F51-F60,2007

Physics

Mathematical Physics

12 pages

Scientific paper

10.1088/1751-8113/40/2/F01

An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two different subsets of N integrals in involution (including the Hamiltonian) can always be explicitly identified. As particular cases, we recover in a straightforward way most of the superintegrability properties of the Smorodinsky-Winternitz and generalized Kepler-Coulomb systems on spaces of constant curvature and we introduce as well new classes of (quasi-maximally) superintegrable potentials on these spaces. Results here presented are a consequence of the sl(2) Poisson coalgebra symmetry of all the Hamiltonians, together with an appropriate use of the phase spaces associated to Poincare and Beltrami coordinates.

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