  We investigate the local non--linear dynamics of irrotational dust with
vanishing magnetic part of the Weyl tensor, $H_{ab}$. Once coded in the initial
conditions, this dynamical restriction is respected by the relativistic
evolution equations. Thus, the outcome of the latter are {\it exact solutions}
for special initial conditions with $H_{ab}=0$, but with no symmetries: they
describe inhomogeneous triaxial dynamics generalizing that of a fluid element
in a Tolman--Bondi, Kantowski--Sachs or Szekeres geometry. A subset of these
solutions may be seen as (special) perturbations of Friedmann models, in the
sense that there are trajectories in phase--space that pass arbitrarily close
to the isotropic ones. We find that the final fate of ever--expanding
configurations is a spherical void, locally corresponding to a Milne universe.
For collapsing configurations we find a whole family of triaxial attractors,
with vanishing local density parameter $\Omega$. These attractors locally
correspond to Kasner vacuum solutions: there is a single physical configuration
collapsing to a degenerate {\it pancake}, while the generic configuration
collapses to a triaxial {\it spindle} singularity. These {\it silent universe}
models may provide a fair representation of the universe on super horizon
scales. Moreover, one might conjecture that the non--local information carried
by $H_{ab}$ becomes negligible during the late highly non--linear stages of
collapse, so that the attractors we find may give all of the relevant expansion
or collapse configurations of irrotational dust.
