Small Oscillations of Collisionless Gravitating Systems
In astrophysics we come across systems like galaxies, and the halos of galaxies, that are made up of a large number of particles. The dominant force in the system is the (smoothed out) gravitational force created by these particles. The evolution of any perturbation on an equilibrium configuration of such a system is described by the collisionless Boltzmann equation for the phase space density function and the Poisson equation for the gravitational field. In this paper we find the qualitative features of the evolution of small perturbations by using methods from the theory of linear operators. We conclude that all such perturbations mix away, for a generic system, by a process analogous to Landau damping, so that the system reaches equilibrium.
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