  We consider the motion of an electron in an atom subjected to a strong
linearly polarized laser field. We identify the invariant structures organizing
a very specific subset of trajectories, namely recollisions. Recollisions are
trajectories which first escape the ionic core (i.e., ionize) and later return
to this ionic core, for instance, to transfer the energy gained during the
large excursion away from the core to bound electrons. We consider the role
played by the directions transverse to the polarization direction in the
recollision process. We compute the family of two-dimensional invariant tori
associated with a specific hyperbolic-elliptic periodic orbit and their stable
and unstable manifolds. We show that these manifolds organize recollisions in
phase space.
