Abstract
We study the orbits near the Lagrangian points L4 and L5 in a rotating model of a barred galaxy. The families of short period orbits (SPO) and long period orbits (LPO) are joined by an infinity of bridges. We study the evolution of these families as the bar perturbation changes. In particular we find the change of the connections between various families at particular collisions of bifurcations. When L4, L5 become unstable the SPO and LPO join away from the Lagrangian points. At the same time the LPO characteristics form spirals or infinite figure eight oscillations on one side of L4 (or L5). An infinity of such spirals are formed by the higher order bifurcations. The similarity with the restricted three body problem (especially the cases µ>µ1 = 0.03852 and µ = 0.5) is pointed out.
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