1998A&A...334..829O

The stability of the Lagrangian points and the vertical periodic orbits around them is examined in the context of barred galaxies. A transition from stability to complex instability appears for the points L₄ and L₅ when the strength of the bar is sufficiently large. The Hopf-like bifurcation associated to such a transition is inverse and its effects on the central family of periodic orbits and neighbouring orbits are described. This instability can play an important role for barred galaxies secularly increasing the strength of their bar, because a sudden full destabilization of matter around these Lagrangian points must occur. This effect is demonstrated with a sample of trajectories diffusing away from the corotation circle several 10kpc radially, and several kpc out the galaxy plane.