Mathematikgebäude, Seminarraum M911

We employ variational methods to find periodic orbits of a charged particle moving under the influence of a magnetic field on a closed Riemannian manifold. In particular, we generalize to our setting two classical results in the theory of standard geodesics due to Lusternik-Fet and to Bangert, respectively.
In the first theorem (with Luca Asselle), we prove that if the ambient manifold is not a K(G,1), then for almost every E>0, there exists a contractible magnetic geodesic with energy E.
In the second theorem (with Luca Asselle, Alberto Abbondandolo, Marco Mazzucchelli, and Iskander Taimanov), we show that if the manifold is a surface and the magnetic field is oscillating, then for almost every small E>0, there exist infinitely many closed magnetic geodesics with energy E.

Im Anschluss findet ein zweiter Vortrag im Oberseminar statt.
Eine Nachsitzung nach dem zweiten Vortrag ist vorgesehen.

Dr. Gabriele Benedetti

Universität Leipzig