The Stability and Vibrations of a Gas of Stars

The initial value problem for a small disturbance from an equilibrium of an encounterless stellar system is discussed. In a spherical cluster small wave-length disturbances damp as the stars become well mixed. In the artificial infinite uniform rotating system we discuss disturbances of all wave-lengths. Jeans' condensational instability is the same as in a collision dominated gas. Landau damping occurs for wave-lengths smaller than the critical one.