Integrable and stochastic behaviour in dynamical astronomy

Some problems of stellar dynamics and celestial mechanics are presented, where integrability and stochasticity play a role. Such problems are: 1) the motions of stars in the meridian plane of an axisymmetric galaxy, 2) the motions in the plane of symmetry of a spiral galaxy, 3) the escapes of stars to infinity, 4) the bifurcations of families of periodic orbits, 5) Lynden-Bell's (1967) statistics in collapsing systems, 6) the general three-body problem, and 7) the applicability of Arnold's (1967) diffusion. (34 refs).