Dynamics of gravitationally interacting systems

A short review of some problems for dynamical and statistical interpretations of the observed properties of elliptical galaxies is presented. N-body numerical simulations of collisionless gravitating systems, undergoing dynamical relaxation to the virial equilibrium, show that if initial conditions are properly chosen, the relaxed density profiles nicely reproduce the real galaxy luminosity profiles. General statistical mechanics arguments fail to provide satisfactory explanation of the galaxy formation mechanisms, but some empirical statistical arguments drawn from numerical simulation data help a better understanding of the collisionless dynamics in systems with long-range interactions.