Self-pulsing effect in chaotic scattering

We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in situations for which a stable island, associated with the inner fundamental periodic orbit of the system exists and is large, but chaos around this island is well developed. Such situations are quite common as they correspond typically to the near-integrable domain in the transition from integrable to chaotic scattering. Both classical and quantum dynamics are analysed and in both cases, the most surprising effect is a periodic response to an incoming wave packet. The period of this self-pulsing effect or scattering echoes coincides with the mean period, by which the scattering trajectories rotate around the stable orbit. This period of rotation is directly related to the development stage of the underlying horseshoe. Therefore the predicted echoes will provide experimental access to topological information. We numerically test these results in kicked one-dimensional models and in open billiards.