JournalsjemsVol. 19, No. 2pp. 551–579

Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level

  • Alberto Abbondandolo

    Universität Bochum, Germany
  • Leonardo Macarini

    Universidade Federal do Rio de Janeiro, Brazil
  • Marco Mazzucchelli

    Université de Lyon, France
  • Gabriel P. Paternain

    University of Cambridge, UK
Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level cover

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Abstract

We consider an exact magnetic ow on the tangent bundle of a closed surface. We prove that for almost every energy level κ\kappa below the Mañé critical value of the universal covering there are in finitely many periodic orbits with energy κ\kappa.

Cite this article

Alberto Abbondandolo, Leonardo Macarini, Marco Mazzucchelli, Gabriel P. Paternain, Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 551–579

DOI 10.4171/JEMS/674