This proposal will study the dynamics of galactic disks as nonlinear dynamical systems using the modal approach. To assure that the modal approach is realistic and viable, a study will be made of the spiral structure of selected galaxies. Thus, the theory will first be applied to the galaxy M81 and the Milky Way for which observational data are already available and certain preliminary studies of spiral modes have also been carried out. Next, the nonlinear interactions of the mildly unstable modes associated with a two-component basic equilibrium state (consisting of stars and interstellar gas) will be considered. This process is expected to be greatly influenced by the gaseous component whose strong nonlinear response, and self-gravitating and dissipative character would tend to stabilize the spiral structure. Finally analytical studies will be made of the various physical processes after these processes have been formulated for mathematical treatment.
