Preprint A149/2002
Periodic orbits for exact magnetic flows on surfaces

Gabriel Paternain | Contreras, Gonzalo | Macarini, Leonardo

**Keywords: **
periodic orbits | magnetic flows | Mane's critical value | Mather-Mane theory

We show that any exact magnetic flow on a closed surface has periodic orbits in
all energy levels.
Moreover, we give homological
and homotopic properties of these periodic orbits in terms of the Ma\~né's
critical values of the corresponding Lagrangian. We also prove that if
$M$ is not the 2-torus
the energy level $k$ is of contact type if and only if $k>c_0$, where
$c_{0}$ is Ma\~né's strict critical value.
When $M$ is the 2-torus we give examples for which the energy level
$c_{0}$ is of contact type.