Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces

@article{Ballesteros2009MaximalSO,
  title={Maximal superintegrability of the generalized Kepler–Coulomb system on N-dimensional curved spaces},
  author={{\'A}ngel Ballesteros and Francisco J. Herranz},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2009},
  volume={42},
  pages={245203}
}
The superposition of the Kepler–Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper, we present the generalization of this result to the N-dimensional spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry approach that makes use of the curvature… 

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References

SHOWING 1-10 OF 70 REFERENCES

Superintegrability on N-dimensional spaces of constant curvature from so(N + 1) and its contractions

The Lie—Poisson algebra so(N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and

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

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

Maximal superintegrability on N-dimensional curved spaces

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.

Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2

The existence of superintegrable systems with n=2 degrees of freedom possessing three independent globally defined constants of motion which are quadratic in the velocities is studied on the

Dynamical symmetries in a spherical geometry. I

The two potentials for which a particle moving non-relativistically in a spherical space under the action of conservative central force executes closed orbits are found. When the curvature is zero

Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2

The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane. First, the theory of central potentials on spaces of

Completeness of multiseparable superintegrability on the complex 2-sphere

The possibility that Schrodinger's equation with a given potential can separate in more than one coordinate system is intimately connected with the notion of superintegrability. Here we demonstrate,

A new superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in three degrees of freedom, obtained as a reduction of pure Keplerian motion in six dimensions. The new Hamiltonian is a generalization of the Keplerian

On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space

We give a graphical prescription for obtaining and characterizing all separable coordinates for which the Schr?dinger equation admits separable solutions for one of the superintegrable potentials
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