Theory of Newtonian self-gravitating stationary spherically symmetric   systems
  We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a region with compact closure.Based on a dynamical systems analysis we derive theorems that guarantee that the steady state solutions have finite mass and compact support. 
J. Mark Heinzle, Alan D. Rendall, Claes Uggla