  We consider a version of the Vlasov equation on the circle under a periodic
potential $V(x,t)$ and a repulsing smooth interaction $W$. We suppose that the
Lagrangian for the single particle has chaotic orbits; using Aubry-Mather
theory and ideas of W. Gangbo, A. Tudorascu and P. Bernard, we prove that, for
any initial distribution of particles, it is possible to choose their initial
speed in such a way to get a chaotic orbit on $[0,+\infty)$.
