R. Guantes et al., PERIODIC-ORBITS AND THE HOMOCLINIC TANGLE IN ATOM-SURFACE CHAOTIC SCATTERING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(1), 1997, pp. 378-389
In this paper the phase-space structure of a realistic chaotic scatter
ing system, namely, the collisions of He atoms off Cu surfaces with di
fferent degrees of corrugation, is investigated. We demonstrate that t
he homoclinic tangle generated by a principal unstable periodic orbit,
which corresponds to the unperturbed motion of the He atom traveling
parallel to the surface in the asymptotic region, determines the entir
e scattering dynamics of the system. The fractal properties and some p
hysical invariant features of the system can be understood using suita
ble Poincare surfaces of section. Moreover, in this paper we also anal
yze in detail the periodic orbit structure in the interaction region,
and show how the homoclinic chaotic trajectories can be organized in a
similar fashion to the well-known Farey tree organization for resonan
ces. The consequences of this analogy for the different scaling laws o
bserved in chaotic scattering problems are discussed.