Commentarii Mathematici Helvetici


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Volume 90, Issue 1, 2015, pp. 155–193
DOI: 10.4171/CMH/350

Published online: 2015-02-23

On the existence of three closed magnetic geodesics for subcritical energies

Alberto Abbondandolo[1], Leonardo Macarini[2] and Gabriel P. Paternain[3]

(1) Ruhr-Universität Bochum, Germany
(2) Universidade Federal do Rio de Janeiro, Brazil
(3) University of Cambridge, United Kingdom

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 $\kappa$. If in addition the energy level is assumed to be non-degenerate we prove existence of infinitely many closed magnetic geodesics.

Keywords: Magnetic geodesic, critical values, energy level

Abbondandolo Alberto, Macarini Leonardo, Paternain Gabriel: On the existence of three closed magnetic geodesics for subcritical energies. Comment. Math. Helv. 90 (2015), 155-193. doi: 10.4171/CMH/350