  We consider how the nature of the dynamics affects ground state properties of
ballistic quantum dots. We find that ``mesoscopic Stoner fluctuations'', that
arise from the residual screened Coulomb interaction, are very sensitive to the
degree of chaos. It leads to ground state energies and spin-polarizations whose
fluctuations strongly increase as a system becomes less chaotic. The crucial
features are illustrated with a model that depends on a parameter that tunes
the dynamics from nearly integrable to mostly chaotic.
