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.

Anexos:

• clor.ps