Non-perturbative features of driven scattering systems
Abstract
We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure where the number Nc of zeros of the solutions plays the role of an order parameter marking the level of the observed self-similar structure. The behavior is understood both in terms of the return map and of the intersections pattern of the invariant manifolds of the outermost fixed points. In the non-periodic case the scattering function does not provide a complete development of the hierarchical structure. The singularities pattern of the outgoing energy as a function of the driver amplitude is connected to the arrangement of gaps in the fundamental regions. The survival probability distribution of temporarily bound orbits is shown to decay asymptotically as a power law. The "stickiness" of regular regions of phase space, given by KAM surfaces and remnant of KAM curves, is responsible for this observation.
Cite
@article{arxiv.1206.1922,
title = {Non-perturbative features of driven scattering systems},
author = {Andrea Cintio and Fulvio Cornolti},
journal= {arXiv preprint arXiv:1206.1922},
year = {2012}
}