Global continuation of a vlasov model of rotating galaxies

A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about 1011 stars. In the astrophysics literature such a galaxy is typically modeled by the VlasovPoisson system. We prove an existence theorem for axisymmetric steady states of galaxies that may rotate rapidly. Such states are given in terms of a fairly general function phi of the particle energy and angular momentum. The set /C of such states form a connected set in an appropriate function space. Along the set /C, we prove under suitable conditions that either (a) the supports of the galaxies become unbounded or (b) both the rotation speeds and the densities somewhere within the galaxy become unbounded.