The phase space structure in the vicinity of vertical Lyapunov orbits around <i>L</i>1,2 in a barred galaxy model

We study the phase space structure and orbital diffusion from vicinity of vertical Lyapunov periodic orbits around unstable Lagrangian points L1,2 in a 3D barred galaxy model. By perturbing initial conditions these orbits, we detected following five types structures 4D spaces section: (i) Ring-like structures, sticky for large time intervals to invariant manifolds simple double orbits. (ii) 2D tori belonging quasi-periodic stable existing region. They are associated either with L4,5 or "stable anomalous" (iii) Orbits tori, forming "sticky tori", before they slowly depart them. (iv) Clouds that have strong chaotic behavior. Such clouds consequents slow speeds, because hindered by presence (v) Toroidal zones consisting stick long on "unstable continuing integration, find eventually become strongly chaotic, retaining however small due anomalous