On the existence of three closed magnetic geodesics for subcritical energies

Abstract

We consider exact magnetic flows on closed orientable surfaces. We show that for almost every energy $\kappa$ below Ma\~n\'e'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.