On the bifurcations of the Vlasov equation

The Vlasov equation appears in a variety of physical situations, the most well-known being plasma physics, where electrons and ions interact through electro-magnetic forces, and self-gravitating systems, where stars – for instance - interact through gravitation.

My goal here is to study the qualitative dynamical behavior of the Vlasov equation, with an emphasis on universal ones, that is, those which do not depend on the underlying physical system. In particular, I will be interested in the bifurcations of the stationary states.

I will first introduce the Vlasov equation, its structure and its dynamical peculiarities (stationary states, Landau damping, for instance), and then turn to the description of certain generic bifurcations, and attempt a classification.