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

Alberto Abbondandolo (1) , Leonardo Macarini (2) , Marco Mazzucchelli (3) , Gabriel P. Paternain (4)

1 Ruhr-Universitat Bochum, Fakultat fur Mathematik
2 UFRJ - Universidade Federal do Rio de Janeiro
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
4 CAM - University of Cambridge [UK]

We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level κ below the Mañé critical value of the universal cover there are infinitely many periodic orbits with energy κ.

Domains: Mathematics [math]

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. Journal of the European Mathematical Society, 2017, 19, pp.551 - 579. ⟨10.4171/JEMS/674⟩. ⟨ensl-01475277⟩