  Two-armed, grand design spirals and inner and outer rings in barred galaxies
can be due to orbits guided by the manifolds emanating from the vicinity of the
L1 and L2 Lagrangian points, located at the ends of the bar. We first summarise
the necessary theoretical background and in particular we describe the dynamics
around the unstable equilibrium points in barred galaxy models, and the
corresponding homoclinic and heteroclinic orbits. We then discuss two specific
morphologies and the circulation of material within the corresponding
manifolds. We also discuss the case where mass concentrations at the end of the
bar can stabilise the L1 and L2 and the relevance of this work to the gas
concentrations in spirals and rings.
