Rings and spirals in barred galaxies. I Building blocks
  In this paper we present building blocks which can explain the formation and properties both of spirals and of inner and outer rings in barred galaxies. We first briefly summarise the main results of the full theoretical description we have given elsewhere, presenting them in a more physical way, aimed to an understanding without the requirement of extended knowledge of dynamical systems or of orbital structure. We introduce in this manner the notion of manifolds, which can be thought of as tubes guiding the orbits. The dynamics of these manifolds can govern the properties of spirals and of inner and outer rings in barred galaxies. We find that the bar strength affects how unstable the L1 and L2 Lagrangian points are, the motion within the 5A5A5Amanifold tubes and the time necessary for particles in a manifold to make a complete turn around the galactic centre. We also show that the strength of the bar, or, to be more precise, of the non-axisymmetric forcing at and somewhat beyond the corotation region, determines the resulting morphology. Thus, less strong bars give rise to R1 rings or pseudorings, while stronger bars drive R2, R1R2 and spiral morphologies. We examine the morphology as a function of the main parameters of the bar and present descriptive two dimensional plots to that avail. We also derive how the manifold morphologies and properties are modified if the L1 and L2 Lagrangian points become stable. Finally, we discuss how dissipation affects the manifold properties and compare the manifolds in gas-like and in stellar cases. Comparison with observations, as well as clear predictions to be tested by observations will be given in an accompanying paper. 
E. Athanassoula, M. Romero-Gomez, J. J. Masdemont