Chaotic Scattering in Several Dimensions

For chaotic scattering in two-degree-of-freedom (N=2), time-independent, Hamiltonian systems, scattering functions (i.e., plots of the dependence of a phase space variable after scattering versus a phase space variable before scattering) typically display singularities on a fractal set. For N#62;2, however, scattering functions typically do not have fractal properties (even when the chaotic invariant set is fractal), unless the fractal dimension of the chaotic set is large enough. A numerical investigation of this phenomenon is presented for a scatterer consisting of four reflecting spheres at the vertices of a regular tetrahedron.