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A maximally superintegrable system on an n-dimensional space of nonconstant curvature

Angel Ballesteros·Alberto Enciso·Francisco J. Herranz·Orlando Ragnisco
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Abstract

A novel Hamiltonian system in n dimensions which admits the maximal number 2n-1 of functionally independent, quadratic first integrals is presented. This system turns out to be the first example of a maximally superintegrable Hamiltonian on an n-dimensional Riemannian space of nonconstant curvature, and it can be interpreted as the intrinsic Smorodinsky-Winternitz system on such a space. Moreover, we provide three different complete sets of integrals in involution and solve the equations of motion in closed form.

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Angel Ballesteros, Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco. 2006-12-26. A maximally superintegrable system on an n-dimensional space of nonconstant curvature. https://doi.org/10.1016/j.physd.2007.09.021

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