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Fundam. Prikl. Mat., 2019, Volume 22, Issue 6, Pages 169–182 (Mi fpm1858)  

Superintegrable Bertrand magnetic geodesic flows

E. A. Kudryavtseva, S. A. Podlipaev

Lomonosov Moscow State University

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
Russian Foundation for Basic Research 19-01-00775_a


Full text: PDF file (178 kB)
UDC: 514.853+517.938.5

Citation: E. A. Kudryavtseva, S. A. Podlipaev, “Superintegrable Bertrand magnetic geodesic flows”, Fundam. Prikl. Mat., 22:6 (2019), 169–182

Citation in format AMSBIB
\Bibitem{KudPod19}
\by E.~A.~Kudryavtseva, S.~A.~Podlipaev
\paper Superintegrable Bertrand magnetic geodesic flows
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 6
\pages 169--182
\mathnet{http://mi.mathnet.ru/fpm1858}


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  • Фундаментальная и прикладная математика
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