On an Integrable Magnetic Geodesic Flow on the Two-torus

    2015, Volume 20, Number 6, pp.  667-678

    Author(s): Taimanov I. A.

    The magnetic geodesic flow on a flat two-torus with the magnetic field $F=\cos(x)dx \wedge dy$ 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 $E \geqslant 1/2$, 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.
    Keywords: integrable system, magnetic geodesic flow
    Citation: Taimanov I. A., On an Integrable Magnetic Geodesic Flow on the Two-torus, Regular and Chaotic Dynamics, 2015, Volume 20, Number 6, pp. 667-678

    Access to the full text on the Springer website