Poincare map for scattering states

Abstract

For scattering states in classical mechanics a map is constructed, which is an analogue to the Poincare map for bound state trajectories. Iteration of this map indicates which parts of the phase space are filled by unstable trajectories that are sensitive to small changes in the initial conditions, and which regions are filled by stable trajectories. Examples for this map are given by numerical calculations for scattering off a simple two-dimensional model potential.