  Both uncorrelated ("sequential") and correlated ("nonsequential") processes
contribute to the double ionization of the helium atom in strong laser pulses.
The double ionization probability has a characteristic "knee" shape as a
function of the intensity of the pulse. We investigate the phase-space dynamics
of this system, specifically by finding the dynamical structures that regulate
the ionization processes. The emerging picture complements the recollision
scenario by clarifying the distinct roles played by the recolliding and core
electrons. Our analysis leads to verifiable predictions of the intensities
where qualitiative changes in ionization occur, leading to the hallmark "knee"
shape.
