Classical Scattering Theory
It was first recognized by Hunziker  that the notions of scattering theory play an important role in classical mechanics. It turned out  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  time delay has a simple geometrical meaning  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.
KeywordsPhase Space Free Motion Canonical Transformation Canonical Coordinate System Negative Time Delay
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