  We investigate chaotic scattering on an attractive step potential with a
quadrupolar deformation. The phase space features of the bound billiard are
studied by using the notion of symmetry lines to find periodic orbits. We show
that the scattering dynamics is intimately linked to structures in the bound
billiard (infinite potential wall) phase space. The existence of preferred
scattering directions is shown to be a consequence of large scale features of
the phase space such as the period-two orbits. Self-similarity in the
scattering functions is directly linked to unstable periodic orbits of the
bound phase space. The main observations and methodology are applicable to
concave billiards in general.
