  We develop an analytical theory of chaotic spiral arms in galaxies. This is
based on the Moser theory of invariant manifolds around unstable periodic
orbits. We apply this theory to the chaotic spiral arms, that start from the
neighborhood of the Lagrangian points L1 and L2 at the end of the bar in a
barred-spiral galaxy. The series representing the invariant manifolds starting
at the Lagrangian points L1, L2, or unstable periodic orbits around L1 and L2,
yield spiral patterns in the configuration space. These series converge in a
domain around every Lagrangian point, called "Moser domain" and represent the
orbits that constitute the chaotic spiral arms. In fact, these orbits are not
only along the invariant manifolds, but also in a domain surrounding the
invariant manifolds. We show further that orbits starting outside the Moser
domain but close to it converge to the boundary of the Moser domain, which acts
as an attractor. These orbits stay for a long time close to the spiral arms
before escaping to infinity.
