Superintegrability and higher-order constants for classical and quantum systems

@article{Kalnins2011SuperintegrabilityAH,
  title={Superintegrability and higher-order constants for classical and quantum systems},
  author={Ernie G. Kalnins and Willard Miller and George S. Pogosyan},
  journal={Physics of Atomic Nuclei},
  year={2011},
  volume={74},
  pages={914-918}
}
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are higher order differential operators than two. Indeed they conjectured that for a general class… 
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