Topology of High-Dimensional Chaotic Scattering

We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.