  The purpose of this paper is to study the relations between different
concepts of dispersive solution for the Vlasov-Poisson system in the
gravitational case. Moreover we give necessary conditions for the existence of
partially and totally dispersive solutions and a sufficient condition for the
occurence of statistical dispersion. These conditions take the form of
inequalities involving the energy, the mass and the momentum of the solution.
Examples of dispersive and non-dispersive solutions--steady states, periodic
solutions and virialized solutions--are also considered.
