Chaotic scattering without chaos—A counterexample

A scattering system is commonly called irregular or chaotic if it has a scattering function which is singular on a fractal. The only previously known mechanism generating such an irregular scattering function rests on the existence of a chaotic bound set in the closure of the set of asymptotically free trajectories. Therefore, it has been generally assumed that the measurement of an irregular scattering function implies the existence of a chaotic bound dynamics which is responsible for the fractal set of singularities. In this paper a counterexample is constructed yielding an integrable and smooth Hamiltonian which has orbiting resonances on a Cantor set. This counterexample shows that the existence of a chaotic bound set is not a necessary condition for irregular scattering. It is possible to have irregular scattering without chaotic bound motion.