Sensitive dependence on impact parameter produces fractal structures in scattering observables
Chaotic scattering occurs when a trajectory can linger arbitrarily long near a chaotic saddle (hyperbolic set) before escaping. The deflection function Θ(b) — the output angle as a function of impact parameter b — develops a fractal Cantor-set structure of singularities where the dwell time diverges. This fractal structure implies that cross-sections contain self-similar features at all scales. The underlying invariant set is a nonattracting strange repeller with fractal dimension d < 1. (Bleher-Ott-Grebogi 1989, Jung 1986)