Classical Scattering Theory

Abstract

It was first recognized by Hunziker [1] that the notions of scattering theory play an important role in classical mechanics. It turned out [2] that it leads to non-trivial information for the global properties of the solutions of the classical trajectories. For instance it shows that in the three body problem there are large regions in phase space with 2n — 1 = 17 constants of motion and all trajectories in this region are homotopic to straight lines. Furthermore Wigner’s [3] time delay has a simple geometrical meaning [4] for the trajectories. For instance it shows that in the three body problem there are large regions in phase space with 2n − 1 = 17 constants of motion and all trajectories in this region are homotopic to straight lines.

Lectures given at the XX. Internationale Universitätswochen für Kernphysik, Schladming, Austria, February 17–26, 1981.