Partitioning the phase space in a natural way for scattering systems.
In this paper, we demonstrate a recent procedure for the construction of a symbolic dynamics for open systems by applying it to a model potential, the driven inverted Gaussian, which has proven very useful in describing laser-atom interaction. The symbolic dynamics and the corresponding partition of the Poincaré map are natural from the point of view of an asymptotic observer since the resulting branching tree coincides with the one extracted from the scattering functions. In general, the whole procedure is approximate because it only describes the globally unstable part of the chaotic invariant set, that is, the part that can be seen by an asymptotic observer in scattering data. It ignores Kolmogorov-Arnold-Moser islands and their fractal surroundings.