Controlling chaotic transport is a key challenge in many branches of physics like particle accelerator physics, free electron lasers or magnetically confined fusion plasmas. One way to control transport would be that of reducing or suppressing chaos. Most of the methods for controlling chaotic systems is done by tilting targeted trajectories. However, for many body experiments like the magnetic confinement of a plasma or the control of turbulent flows, such methods are hopeless due to the high number of trajectories to deal with simultaneously. For these systems, it is desirable to control transport properties without significantly altering the original system under investigation nor its overall chaotic structure. Here we focus on a different strategy which aims at modifying the phase space structures by adding a small apt perturbation or by tuning appropriately the parameters.

One of the most striking surprises of recent years in intense laser-matter interactions has come from multiple ionization by intense short laser pulses: Correlated (nonsequential) double ionization rates were found to be several orders of magnitude higher than the uncorrelated sequential mechanism allows. This discrepancy has made the characteristic ‘‘knee’’ shape in the double ionization yield versus intensity plot into one of the most dramatic manifestations of electron-electron correlation in nature. We investigate the nonlinear dynamics of these systems and relate the qualitative changes observed in the double ionization probability versus intensity plots to phase space structures and their bifurcations. In this way, we identify the phase space structures that regulate atomic double ionization in strong ultrashort laser pulses.