Universität Augsburg
Institut für Mathematik

The contact type conjecture states that low energy hypersurfaces of Hamiltonian systems are not of contact type; and traces back to the 1998 work of Contreras, Iturriaga, Paternain, and Paternain.
We will present the construction (on any closed manifold) of a class of exact magnetic systems, called magnetic systems of strong geodesic type, for which that conjecture holds.
Indeed, for each such system, there exists at least one null-homologous embedded periodic orbit on every energy level, with negative action for energies below the strict Mañé critical value. As a consequence, the corresponding energy surfaces are not of contact type below this threshold.
We also note that the space of such systems on a given closed manifold is infinite dimensional by construction, and that rich multiplicity results hold (ensuring for example arbitrarily many embedded null-homologous periodic magnetic geodesics at each energy level.)

This talk is based on joint work with L. Maier and T. Stalljohann.