Symmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.