Zoll magnetic flows

The focus of the talk, which reports on joint work with Jungsoo Kang and Luca Asselle, are magnetic flows on closed surfaces. First, we discuss integrable examples and their relation with the magnetic curvature. Second, we concentrate on the subclass of Zoll systems, for which all orbits are closed and with same action. In this case, there is an algebraic relation between the action value and the magnetic volume of the system. If we slightly perturb the Zoll system, this relation turns into a so-called systolic inequality, namely into an upper bound on the minimal actionof a closed orbit in terms of the magnetic volume.