  It has recently been shown, in flat Robertson-Walker geometries, that the
dynamics of gravitational actions which are minimally coupled to matter fields
leads to the appearance of "attractors" - sets of physical observables on which
phase space measures become peaked. These attractors will be examined in the
context of inhomogeneous perturbations about the FRW background and in the
context of anisotropic Bianchi I systems. We show that maximally expanding
solutions are generically attractors, i.e. any measure based on phase-space
observables becomes sharply peaked about those solutions which have $P=-\rho$.
