Top: Projection (y,ẏ, with x = 0 and $\dot{x}<0$) of the 4D PSS of 3D sticky chaotic orbits having initially a small z component (z = 0.02) and lying above the planar unstable asymptotic manifolds of successive chaotic regions (in colour). The PSS of the planar orbits is in black. Bottom: Apocentric sections on the configuration space x − y of the 3D chaotic orbits corresponding to the same colours as in the top of this figure. They support the envelope of the bar as well as ring-like structures of R₁ type that fill a small region around the bar. The planar unstable apocentric manifolds of orbits with initial conditions in the chaotic region of the 2D PSS outside the last KAM curve are in black. The energy level is E_j = −4.0.