Higher-order superintegrability of a Holt related potential

Abstract

In a recent paper, Post and Winternitz studied the properties of two-dimensional Euclidean potentials that are linear in one of the two Cartesian variables. In particular, they proved the existence of a potential endowed with an integral of third-order and an integral of fourth-order. In this paper we show that these results can be obtained in a more simple and direct way by noting that this potential is directly related with the Holt potential. It is proved that the existence of a potential with higher order superintegrability is a direct consequence of the integrability of the family of Holt type potentials.

arXiv commentto appear in J. of Phys. A (2013)

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Cited by in corpus (7)

• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• On superintegrable systems separable in Cartesian coordinates
• Geometry of Lie integrability by quadratures
• New infinite families of $N$th-order superintegrable systems separating in Cartesian coordinates
• Transformation of the Stackel matrices preserving superintegrability
• Integrable systems in magnetic fields: the generalized parabolic cylindrical case
• Superintegrable systems with position dependent mass: master symmetry and action-angle methods