Examples of complete solvability of 2D classical superintegrable systems

@article{Chen2015ExamplesOC,
  title={Examples of complete solvability of 2D classical superintegrable systems},
  author={Yuxuan Chen and Ernest G. Kalnins and Qiushi Li and Willard Miller},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2015},
  volume={11},
  pages={088}
}
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved algebraically. In this paper we show explicitly, mostly through examples of 2nd order superintegrable systems in 2 dimensions, how the trajectories can be determined in detail using rather elementary algebraic, geometric and analytic methods applied to the closed… 
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