JournalscmhVol. 90, No. 1pp. 155–193

On the existence of three closed magnetic geodesics for subcritical energies

  • Alberto Abbondandolo

    Ruhr-Universität Bochum, Germany
  • Leonardo Macarini

    Universidade Federal do Rio de Janeiro, Brazil
  • Gabriel P. Paternain

    University of Cambridge, United Kingdom
On the existence of three closed magnetic geodesics for subcritical energies cover
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Abstract

We consider exact magnetic flows on closed orientable surfaces. We show that for almost every energy  below Mañé’s critical value of the universal covering there are always at least three distinct closed magnetic geodesics with energy κ\kappa. If in addition the energy level is assumed to be non-degenerate we prove existence of infinitely many closed magnetic geodesics.

Cite this article

Alberto Abbondandolo, Leonardo Macarini, Gabriel P. Paternain, On the existence of three closed magnetic geodesics for subcritical energies. Comment. Math. Helv. 90 (2015), no. 1, pp. 155–193

DOI 10.4171/CMH/350