Symplectic coarse graining approach to the dynamics of spherical
  self-gravitating systems
  We investigate the evolution of the phase-space distribution function around
slightly perturbed stationary states and the process of violent relaxation in
the context of the dissipationless collapse of an isolated spherical
self-gravitating system. By means of the recently introduced symplectic coarse
graining technique, we obtain an effective evolution equation that allows us to
compute the scaling of the frequencies around a stationary state, as well as
the damping times of Fourier modes of the distribution function, with the
magnitude of the Fourier $k-$vectors themselves. We compare our analytical
results with $N$-body simulations.
