Periodic Orbits of Twisted Geodesic Flows and Floer Homology

Basak Gurel
Centre de Recherches Math., Universite de Montreal

The existence problem for periodic orbits is one of the central questions in Hamiltonian dynamical systems. For systems describing the motion of a charged particle in a magnetic field, i.e., for the so-called twisted geodesic flows, this question was first addressed by V.I. Arnold in the early 80s. Arnold's work initiated an extensive study of the existence problem for periodic orbits of twisted geodesic flows via variational and dynamical systems methods as well as in the context of symplectic topology. In this talk we will discuss various aspects of this problem and related results, focusing, in particular, on recent theorems obtained by symplectic topological (or, more precisely, Floer homological) methods.