Pseudo-proper elements (dots) of orbits inside the J2:1 commen-surability obtained by the SWIFT package. The black crosses mark their initial conditions with 𝑔₁ – 𝑔₂ ≈ 0 (𝑔₁ – 𝑔₂ = π) in the left (right) frame. The section Q₂ ≈ 0 (Q₂ ≈ π) in Eq. (23) is used to record the pseudo-proper elements of each orbit in frame a (frame b). The colored (gray) dots mark the pseudo-proper elements of orbits trapped (not trapped) in the v₅ libration domain.