  We present a global approach of non-dissipative physics. Based on symplectic
mechanics this technique allows us to obtain the solution of a very large class
of problems in terms of a Taylor expand. We apply this method to the problem of
gravitational instability and we obtain a general expression of the
gravitational potential, solution of the Vlasov- Poisson gravitational
potential, solution of the Vlasov-Poisson system, as a function of time in the
context of Newtonian dust cosmology.
