  We study the dynamics near the unstable Lagrangian points in galactic bar
models using dynamical system tools in order to determine the global morphology
of a barred galaxy. We aim at the case of non-autonomous models, in particular
with secular evolution, by allowing the bar pattern speed to decrease with
time. We extend the concept of manifolds widely used in the autonomous problem
to the Lagrangian Coherent Structures (LCS), widely used in fluid dynamics,
which behave similar to the invariant manifolds driving the motion. After
adapting the LCS computation code to the galactic dynamics problem, we apply it
to both the autonomous and non-autonomous problems, relating the results with
the manifolds and identifying the objects that best describe the motion in the
non-autonomous case. We see that the strainlines coincide with the first
intersection of the stable manifold when applied to the autonomous case, while,
when the secular model is used, the strainlines still show the regions of
maximal repulsion associated to both the corresponding stable manifolds and
regions with a steep change of energy. The global morphology of the galaxy
predicted by the autonomous problem remains unchanged.
