The manifold theory has many interesting applications in Celestial Mechanics as well as in Dynamical Astronomy. The unstable manifolds of the unstable Lagrangian points L1 and L2 as well as of all the unstable periodic orbits around the region of corotation, of a 2-D Hamiltonian of a barred spiral galaxy, define the paths along which all the chaotic orbits will move before escaping from the system. Chaos in this case is weak and can be described by analytical convergent series, as it was proven by Moser, something that was not expected. The Moser domain of convergence of these analytical series has a spiral shape when projected on the configuration space of the galaxy and moreover it acts as an attractor for chaotic orbits outside it. This is a way to explain the “stickiness” of chaotic orbits along the unstable manifolds for long enough time. Therefore, the manifold theory gives a reliable explanation why chaotic orbits can support spiral structures in real barred spiral galaxies.