The eigenvalue problem for integrable gravitating systems with application to galactic discs

A new statement of the eigenvalue problem of studying small perturbations in arbitrary integrable self-gravitating systems is presented. An example of such a system, a 2D stellar disc, is considered in detail. The theory, based on the general equation for disc eigenmodes, reveals mechanisms for the formation and growth of global galactic structures. This new point of view specifies the limits of the unified theory of bar-like and spiral modes that was based on the assumption that global galactic structures could be understood in terms of low-frequency disc modes.