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arXiv · 1504.04293

Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability

Manuel F. Ranada
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Abstract

The superintegrability of four Hamiltonians $\tilde{H_r} = λ\, H_r$, $r=a,b,c,d$, where $H_r$ are known Hamiltonians and $λ$ is a certain function defined on the configuration space and depending of a parameter $κ$, is studied. The new Hamiltonians, and the associated constants of motion $J_{ri}$, $i=1,2,3$, are continous functions of the parameter $κ$. The first part is concerned with separability and quadratic superintegrability (the integrals of motion are quadratic in the momenta) and the second part is devoted to the existence of higher-order superintegrability. The results obtained in the second part are related with the TTW and the PW systems.

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Manuel F. Ranada. 2015-04-16. Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability. https://doi.org/10.1063/1.4918611

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