  We study the ergodic properties of a two-dimensional self-gravitating system
using molecular dynamics simulations. We apply three different tests for
ergodicity: a direct method comparing the time average of a particle momentum
and position to the respective ensemble average, sojourn times statistics and
the dynamical functional method. For comparison purposes they are also applied
to a short-range interacting system and to the Hamiltonian mean-field model.
Our results show that a two-dimensional self-gravitating system takes a very
long time to establish ergodicity. If a Kac factor is used in the potential
energy, such that the total energy is extensive, then this time is independent
of particle number, and diverges with $\sqrt{N}$ without a Kac factor.
