  Numerical evidence is given that spherically symmetric perturbations of
stable spherically symmetric steady states of the gravitational Vlasov-Poisson
system lead to solutions which oscillate in time. The oscillations can be
periodic in time or damped. Along one-parameter families of polytropic steady
states we establish an Eddington-Ritter type relation which relates the period
of the oscillation to the central density of the steady state. The numerically
obtained periods are used to estimate possible periods for typical elliptical
galaxies.
