Billiards in a potential:
variational methods, periodic orbits and KAM tori

N. Berglund
preprint IPT-EPFL (1996)

We consider the classical motion of a particle in a plane domain, under the influence of a perpendicular magnetic field and a smooth potential, with elastic reflections on the walls of the domain. We discuss a variational method for finding periodic orbits, determining their stability and proving the existence of KAM tori. This method is applied to a circular scatterer in crossed electromagnetic fields, where we prove the existence of a set of bound states with positive measure, for sufficiently small electric field and low or moderate magnetic field.

Key words: billiards, magnetic field, twist map, chaotic scattering, KAM-theory

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