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arXiv · 1108.5189

Integrable generalizations of oscillator and Coulomb systems via action-angle variables

Tigran Hakobyan·Olaf Lechtenfeld·Armen Nersessian·Armen Saghatelian·Vahagn Yeghikyan
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Abstract

Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N-1)-dimensional system. We present the action-angle formulation of such models in terms of theradial degree of freedom and the action-angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion.

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Tigran Hakobyan, Olaf Lechtenfeld, Armen Nersessian, Armen Saghatelian, Vahagn Yeghikyan. 2011-08-25. Integrable generalizations of oscillator and Coulomb systems via action-angle variables. https://doi.org/10.1016/j.physleta.2011.12.034

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