TRANSITION TO CHAOTIC SCATTERING

This paper addresses the question of how chaotic scattering arises and evolves as a system parameter is continuously varied starting from a value for which the scattering is regular (i.e., not chaotic). Our results show that the transition from regular to chaotic scattering can occur via a saddle-center bifurcation, with further qualitative changes in the chaotic set resulting from a sequence of homoclinic and heteroclinic intersections. We also show that a state of "fully developed" chaotic scattering can be reached in our system through a process analogous to the formation of a Smale horseshoe. By fully developed chaotic scattering, we mean that the chaotic-invariant set is hyperbolic, and we find for our problem that all bounded orbits can be coded by a full shift on three symbols. Observable consequences related to qualitative changes in the chaotic set are also discussed.