  We analyze the dynamical processes behind delayed double ionization of atoms
subjected to strong laser pulses. Using reduced models, we show that these
processes are a signature of Hamiltonian chaos which results from the
competition between the laser field and the Coulomb attraction to the nucleus.
In particular, we exhibit the paramount role of the unstable manifold of
selected periodic orbits which lead to a delay in these double ionizations.
Among delayed double ionizations, we consider the case of "Recollision
Excitation with Subsequent Ionization" (RESI) and, as a hallmark of this
mechanism, we predict oscillations in the ratio of RESI to double ionization
yields versus laser intensity. We discuss the significance of the
dimensionality of the reduced models for the analysis of the dynamical
processes behind delayed double ionization.
