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arXiv · 2001.05067

Superintegrable Bertrand magnetic geodesic flows

Elena A. Kudryavtseva·Sergey A. Podlipaev
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Abstract

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 metric has a constant scalar curvature and the magnetic field is homogeneous, i.e. proportional to the area form.

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BibTeXRIS

Elena A. Kudryavtseva, Sergey A. Podlipaev. 2020-01-14. Superintegrable Bertrand magnetic geodesic flows. https://doi.org/10.1007/s10958-021-05654-2

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