Superintegrable Bertrand Magnetic Geodesic Flows

@article{Kudryavtseva2020SuperintegrableBM,
  title={Superintegrable Bertrand Magnetic Geodesic Flows},
  author={Elena A. Kudryavtseva and S. A. Podlipaev},
  journal={Journal of Mathematical Sciences},
  year={2020},
  volume={259},
  pages={689 - 698}
}
The problem of description of superintegrable systems (i.e., systems with closed trajectories in a certain domain) in the class of rotationally symmetric natural mechanical systems goes back to Bertrand and Darboux. We describe all superintegrable (in a domain of slow motions) systems in the class of rotationally symmetric magnetic geodesic flows. We show that all sufficiently slow motions in a central magnetic field on a two-dimensional manifold of revolution are periodic if and only if the… 
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Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems

Abstract We prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of invariant…

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