Hidden symmetry and potential group of the Maxwell fish-eye

@article{Frank1990HiddenSA,
  title={Hidden symmetry and potential group of the Maxwell fish-eye},
  author={Alejandro Frank and Francois Leyvraz and Kurt Bernardo Wolf},
  journal={Journal of Mathematical Physics},
  year={1990},
  volume={31},
  pages={2757-2768}
}
The Maxwell fish‐eye is an exceptional optical system that shares with the Kepler problem and the point rotor (mass point on a sphere) a hidden, higher rotation symmetry. The Hamiltonian is proportional to the Casimir invariant. The well‐known stereographic map is extended to canonical transformations between of the phase spaces of the constrained rotor and the fish‐eye. Their dynamical group is a pseudoorthogonal one that permits a succint ‘‘4π’’ wavization of the constrained system. The fish… 

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