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On an integrable magnetic geodesic flow on the two-torus

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Abstract

The magnetic geodesic flow on a flat two-torus with the magnetic field F = cos(x)dx ∧ dy is completely integrated and the description of all contractible periodic magnetic geodesics is given. It is shown that there are no such geodesics for energy E ≥ 1/2, for E < 1/2 simple periodic magnetic geodesics form two S 1-families for which the (fixed energy) action functional is positive and therefore there are no periodic magnetic geodesics for which the action functional is negative.

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  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    Iskander A. Taimanov

  2. Department of Mechanics and Mathematics, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    Iskander A. Taimanov

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Taimanov, I.A. On an integrable magnetic geodesic flow on the two-torus. Regul. Chaot. Dyn. 20, 667–678 (2015). https://doi.org/10.1134/S1560354715060039

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  • DOI: https://doi.org/10.1134/S1560354715060039

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