  A theory is developed for the dynamics of eccentric perturbations $[\propto
\exp(\pm i\phi)]$ of a disk galaxy residing in a spherical dark matter halo and
including a spherical bulge component. The disk is represented as a large
number $N$ of rings with shifted centers and with perturbed azimuthal matter
distributions. Account is taken of the dynamics of the shift of the matter at
the galaxy's center which may include a massive black hole. The gravitational
interactions between the rings and between the rings and the center is fully
accounted for, but the halo and bulge components are treated as passive
gravitational field sources. Equations of motion and a Lagrangian are derived
for the ring + center system, and these lead to total energy and total angular
momentum constants of the motion. We study the eccentric dynamics of a disk
with an exponential surface density distribution represented by a large number
of rings. The inner part of the disk is found to be strongly unstable. Angular
momentum of the rings is transferred outward and to the central mass if
present, and a trailing one-armed spiral wave is formed in the disk. We also
analyze a disk with a modified exponential density distribution where the
density of the inner part of the disk is reduced. In this case we find much
slower, linear growth of the eccentric motion. A trailing one-armed spiral wave
forms in the disk and becomes more tightly wrapped as time increases. The
motion of the central mass if present is small compared with that of the disk.
