Stationary and static stellar dynamic models with axial symmetry

We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry. Using the implicit function theorem we show that certain stationary, spherically symmetric solutions can be embedded in one parameter families of stationary, axially symmetric solutions with finite radius and finite mass. In general, these new steady states have non-vanishing average velocity field, but they can also be constructed such that their velocity field does vanish, in which case they are called static.