Galactic and stellar dynamics: Limits and perspectives

An elementary review about stellar and galactic dynamics is presented. Desp ite involving extremely classical Newtonian physics, stellar dynamics prese nts some fundamental difficulties rarely discussed in the literature, such as why the phase space distribution is assumed to be a smooth function of c oordinates. Many systems are found to be unstable over intermediate time-sc ales, as more instabilities have been discovered over the years, so the old aim of describing equilibrium stable systems shifts presently toward under standing evolutive systems. From the linearized variational Boltzmann equat ion a distinction can be made between instabilities triggered by the chaoti c part of phase space, and instabilities caused by steep gradients in the v elocity part of the distribution function. The new challenges to include ev olutive systems can presently only be studied efficiently with computer tec hniques. Future studies are likely to involve orders of magnitude more adva nced computers in which parallelism will play a major role.