  We propose a new theory to explain the formation of spiral arms and of all
types of outer rings in barred galaxies. We have extended and applied the
technique used in celestial mechanics to compute transfer orbits. Thus, our
theory is based on the chaotic orbital motion driven by the invariant manifolds
associated to the periodic orbits around the hyperbolic equilibrium points. In
particular, spiral arms and outer rings are related to the presence of
heteroclinic or homoclinic orbits. Thus, R1 rings are associated to the
presence of heteroclinic orbits, while R1R2 rings are associated to the
presence of homoclinic orbits. Spiral arms and R2 rings, however, appear when
there exist neither heteroclinic nor homoclinic orbits. We examine the
parameter space of three realistic, yet simple, barred galaxy models and
discuss the formation of the different morphologies according to the properties
of the galaxy model. The different morphologies arise from differences in the
dynamical parameters of the galaxy.
