Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties

@article{Kalnins2007Nondegenerate2C,
  title={Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties},
  author={Ernest G. Kalnins and Jonathan M. Kress and Willard Miller},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2007},
  volume={40},
  pages={3399 - 3411}
}
A classical (or quantum) superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n − 1 functionally independent constants of the motion polynomial in the momenta, the maximum possible. If the constants are all quadratic the system is second-order superintegrable. The Kepler–Coulomb system is the best known example. Such systems have remarkable properties: multi-integrability and multi-separability, an algebra of higher order symmetries whose… 

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