Dynamical map on the parametric plane Ω _bar–M _bar for the orbit with initial conditions , p_R = 0 and V_θ = V _rot(R _bar), representative of the bar structure. The light grey tones represent regular orbits, while increasingly dark tones correspond to increasing instabilities and chaotic motion. The red-hatched regions contain strongly unstable and escaping orbits. We see that, in order to have stability, one must always have M _bar < 10¹⁰ M _⊙. This value decreases with Ω _bar. For high values of Ω _bar, the region with M _bar ~ 10⁹ M _⊙ is unstable.