Dynamics of Silent Universes with and without Lambda

We present results on the non-linear dynamics of a wide class of inhomogeneous cosmological models with irrotational dust and vanishing magnetic part of the Weyl tensor, with and without a cosmological constant Lambda. For a non vanishing Lambda, the study of these models is relevant in the early universe: we find that the expanding regions always inflate and finally isotropize, i.e. de Sitter is the unique attractor. There are however regions that can recollapse, even after the inflationary phase. In this case Lambda becomes negligible and the attractor is the same as for the Lambda=0 case: we find that collapsing regions always fall in filamentary spindle singularities. For Lambda=0, we also find that the expanding regions tend to locally spherical voids. We end with a brief discussion of how these results with Lambda=0 could be relevant for structure formation in the present matter dominated era