Structure formation beyond shell-crossing: nonperturbative expansions
  and late-time attractors
  Structure formation in 1+1 dimensions is considered, with emphasis on the
effects of shell-crossing. The breakdown of the perturbative expansion beyond
shell-crossing is discussed, and it is shown, in a simple example, that the
perturbative series can be extended to a transseries including nonperturbative
terms. The latter converges to the exact result well beyond the range of
validity of perturbation theory. The crucial role of the divergences induced by
shell-crossing is discussed. They provide constraints on the structure of the
transseries and act as a bridge between the perturbative and the
nonperturbative sectors. Then, we show that the dynamics in the deep
multistreaming regime is governed by attractors. In the case of simple initial
conditions, these attractors coincide with the asymptotic configurations of the
adhesion model, but in general they may differ. These results are applied to a
cosmological setting, and an algorithm to build the attractor solution starting
from the Zel'dovich approximation is developed. Finally, this algorithm is
applied to the search of `haloes' and the results are compared with those
obtained from the exact dynamical equations.
