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arXiv · 1209.1314

Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

V. Ayadi·L. Feher·T. F. Gorbe
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Abstract

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.

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V. Ayadi, L. Feher, T. F. Gorbe. 2012-09-06. Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals. https://doi.org/10.7546/jgsp-27-2012-27-44

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