  Linear theory is used to determine the stability of the self-gravitating,
rapidly (and nonuniformly) rotating, two-dimensional, and collisional
particulate disk against small-amplitude gravity perturbations. A gas-kinetic
theory approach is used by exploring the combined system of the Boltzmann and
the Poisson equations. The effects of physical collisions between particles are
taken into account by using in the Boltzmann kinetic equation a Krook model
integral of collisions modified to allow collisions to be inelastic. It is
shown that as a direct result of the classical Jeans instability and a secular
dissipative-type instability of small-amplitude gravity disturbances (e.g.
those produced by a spontaneous perturbation and/or a companion system) the
disk is subdivided into numerous irregular ringlets, with size and spacing of
the order of the Jeans length (= (4-6) mean epicyclic radius). The present
research is aimed above all at explaining the origin of various structures in
highly flattened, rapidly rotating systems of mutually gravitating particles.
In particular, it is suggested that forthcoming Cassini spacecraft
high-resolution images may reveal this kind of hyperfine of the order of 100 m
structure in the main rings A, B, and C of the Saturnian ring system.
