A symplectic approach to gravitational instability

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.