Self-gravitating systems have acquired growing interest in statistical
mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual
approach of statistical mechanics cannot be applied to a system of many point
particles interacting with the Newtonian potential, because of (i) the long
range nature of the 1/r potential and of (ii) the divergence at the origin. We
study numerically the evolutionary behavior of self-gravitating systems with
periodical boundary conditions, starting from simple initial conditions. We do
not consider in the simulations additional effects as the (cosmological) metric
expansion and/or sophisticated initial conditions, since we are interested
whether and how gravity by itself can produce clustered structures. We are able
to identify well defined correlation properties during the evolution of the
system, which seem to show a well defined thermodynamic limit, as opposed to
the properties of the ``equilibrium state''.
Gravity-induced clustering also shows interesting self-similar
characteristics.Comment: 6 pages, 5 figures. To be published on Physica
