Trapping scaling for bifurcations in Vlasov systems

We study non oscillating bifurcations of non homogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. We show that resonances are strongly suppressed, leading to very different phenomena with respect to the homogeneous case. Through an unstable manifold expansion, we show that the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude -generalizing the "trapping scaling" of plasma physics- or may grow to produce a large scale modification of the system. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.