On the origin of rR_1 ring structures in barred galaxies
  We propose a new theory for the formation of rR_1 ring structures, i.e. for ring structures with both an inner and an outer ring, the latter having the form of ``8''. We propose that these rings are formed by material from the stable and unstable invariant manifolds associated with the Lyapunov orbits around the equilibrium points of a barred galaxy. We discuss the shape and velocity structure of the rings thus formed and argue that they are in agreement with the observed properties of rR_1 structures. 
M. Romero-Gomez, J.J. Masdemont, E. Athanassoula, C. Garcia-Gomez