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

From Manifolds to Lagrangian Coherent Structures in galactic bar models