Construction of a natural partition of incomplete horseshoes

We present a method for constructing a partition of an incomplete horseshoe in a Poincare map. The partition is based only on the unstable manifolds of the outermost fixed points and eventually their limits. Consequently, this partition becomes natural from the point of view of asymptotic scattering observations. The symbolic dynamics derived from this partition coincides with the one derived from the hierarchical structure of the singularities of the scattering functions.