Vlasov-like equations, e.g. Vlasov Poisson Equation; 2D Euler; and the Hamiltonian mean field model (HMF) are non-linear Liouville equations with a mean-field Hamiltonian. For first I'll make a short review of known rigorous results about asymptotic behavior of the solutions of these systems: i.e. stationary solutions, BGK waves and Landau Damping. Then I'll present some conjectures on their long time behavior. Finally I'll discuss the possibility of building Eulerian periodic, and Langrangian chaotic, solutions for Vlasov like equations in the spirit of Morita and Kaneco 2006.