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Periodic magnetic geodesics on almost every energy level via variational methods

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Abstract

For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy level the principle of throwing out cycles gives periodic magnetic geodesics on the critical levels defined by the “thrown out” cycles.

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Authors and Affiliations

  1. S.L. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

    I. A. Taimanov

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  1. I. A. Taimanov
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Correspondence to I. A. Taimanov.

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The work was supported by RFBR (grant 09-01-12130-ofi-m) and Max Planck Institute for Mathematics in Bonn.

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Taimanov, I.A. Periodic magnetic geodesics on almost every energy level via variational methods. Regul. Chaot. Dyn. 15, 598–605 (2010). https://doi.org/10.1134/S1560354710040131

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  • DOI: https://doi.org/10.1134/S1560354710040131

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