Top: The (y,ẏ, with x = 0 and $\dot{x}<0$) projection of the 4D PSS of 3D sticky chaotic orbits having a small z component (z = 0.02) initially and lying above the planar unstable asymptotic manifolds of a chaotic region near the border of regular motion (in magenta). The planar PL₂ family is stable in this energy level. The PSS of the planar orbits is in black. Bottom: The apocentric sections of the chaotic orbits (in magenta) plotted above with the same colours, on the x − y plane. These support a ring-like structure of R₁ type that fill a small region around the bar. The planar unstable manifold of orbits outside the last KAM curve is in black. The energy level is E_j = −3.5.