  In a previous paper (Voglis et al. 2006a, paper I) we demonstrated that, in a
rotating galaxy with a strong bar, the unstable asymptotic manifolds of the
short period family of unstable periodic orbits around the Lagrangian points
L$_1$ or L$_2$ create correlations among the apocentric positions of many
chaotic orbits, thus supporting a {\it spiral} structure beyond the bar. In the
present paper we present evidence that the unstable manifolds of {\it all} the
families of unstable periodic orbits near and beyond corotation contribute to
the same phenomenon. Our results refer to a N-Body simulation, a number of
drawbacks of which, as well as the reasons why these do not significantly
affect the main results, are discussed. We explain the dynamical importance of
the invariant manifolds as due to the fact that they produce a phenomenon of
`stickiness' slowing down the rate of chaotic escape in an otherwise
non-compact region of the phase space. We find a stickiness time of order 100
dynamical periods, which is sufficient to support a long-living spiral
structure. Manifolds of different families become important at different ranges
of values of the Jacobi constant. The projections of the manifolds of all the
different families in the configuration space produce a pattern due to the
`coalescence' of the invariant manifolds. This follows closely the maxima of
the observed $m=2$ component near and beyond corotation. Thus, the manifolds
support both the outer edge of the bar and the spiral arms.
