Classical and quantum dynamics for two dimensional electromagnetic potentials asymptotically homogeneous of degree zero

We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting) Lorentz force(defined for velocities that are purely radial) has a finite number of zeros at fixed energy. Any such zero defines a channel, and to the "stable'' ones we associate in quantum mechanics wave operators. Their completeness is studied in the case of zero magnetic flux. In cooperation with Ira Herbst, University of Virginia and with Erik Skibsted, Aarhus University