VERTICAL ORBITAL STRUCTURE AROUND THE LAGRANGIAN POINTS IN BARRED GALAXIES - LINK WITH THE SECULAR EVOLUTION OF GALAXIES

The stability of the Lagrangian points and the vertical periodic orbit s around them is examined in the context of barred galaxies. A transit ion from stability to complex instability appears for the points L-4 a nd L-5 when the strength of the bar is sufficiently large. The Hopf-li ke bifurcation associated to such a transition is inverse and its effe cts on the central family of periodic orbits and neighbouring orbits a re described. This instability can play an important role for barred g alaxies secularly increasing the strength of their bar, because a sudd en full destabilization of matter around these Lagrangian points must occur. This effect is demonstrated with a sample of trajectories diffu sing away from the corotation circle several 10 kpc radially, and seve ral kpc out the galaxy plane.