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Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level

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Abstract

In this paper we consider oscillating non-exact magnetic fields on surfaces with genus at least two and show that for almost every energy level \(k\) below a certain value \(\tau _+^*(g,\sigma )\) less than or equal to the Mañé critical value of the universal cover there are infinitely many closed magnetic geodesics with energy \(k\).

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Acknowledgments

We are very grateful to our PhD advisors, A. Abbondandolo and G. P. Paternain respectively, for many fruitful discussions. We warmly thank the referee for carefully reading the draft and for suggesting various modifications which allowed us to improve the paper.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, NA 4/35, 44780, Bochum, Germany

    Luca Asselle

  2. Mathematisches Institut, WWU Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Gabriele Benedetti

Authors
  1. Luca Asselle
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  2. Gabriele Benedetti
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Correspondence to Gabriele Benedetti.

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Communicated by M. Struwe.

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Asselle, L., Benedetti, G. Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level. Calc. Var. 54, 1525–1545 (2015). https://doi.org/10.1007/s00526-015-0834-1

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  • DOI: https://doi.org/10.1007/s00526-015-0834-1

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