We
consider a particle on a closed Riemannian manifold subject to a
potential (coming, e.g., from an electric or gravitational force
field) and a magnetic field. It is known that if the particle is not
charged, then every energy level of the associated Hamiltonian
system carries a periodic orbit.
If the particle is charged, we shall see that the same holds true for
almost every small enough energy level. Moreover, similar results hold
if the manifold is open and the potential is proper.
