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

Alberto Abbondandolo, Leonardo Macarini, Marco Mazzucchelli, Gabriel P. Paternain

Published 2014-04-30, updated 2015-09-01Version 2

We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level $\kappa$ below the Ma\~n\'e critical value of the universal covering there are infinitely many periodic orbits with energy $\kappa$.