Oscillating solutions of the Vlasov-Poisson system -- A numerical investigation

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.