In this note we show the existence of at least three closed orbits for a charged particle moving on a torus under the influence of a magnetic field together with a potential force.
The result of this note solves a problem, posed by Arnold in 1988, asking to verify the existence of at least three closed orbits for a particle whose trajectories on the 2-torus have a prescribed geodesic curvature, the latter computed relative to a given Riemannian metric.