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arXiv · 2101.05270

Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity

G. Gubbiotti·M. C. Nucci
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Abstract

Nineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick systems [A. Ballesteros, A. Enciso, F.J. Herranz and O. Ragnisco, Class. Quantum Grav. 25, 165005 (2008)], the Taub-NUT system [A. Ballesteros, A. Enciso, F.J. Herranz, O. Ragnisco, and D. Riglioni, SIGMA 7, 048 (2011)], and all the seventeen superintegrable systems for the four types of Darboux spaces as determined in [E.G. Kalnins, J.M. Kress, W. Miller, P. Winternitz, J. Math. Phys. 44, 5811--5848 (2003)].

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G. Gubbiotti, M. C. Nucci. 2021-01-13. Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity. https://doi.org/10.1063/5.0041130

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