Left panel: trajectory of a Type-P particle associated with Set 3 of N-body simulations in the (Ω₂, i₂) plane (black curve). The initial orbital elements of this particle are a₂ = 38.098 au, e₂ = 0.676, i₂ = 18.455°, ω₂ = 134.168°, and Ω₂ = 119.149°. The inner Jupiter-mass planet of such a system has a semimajor axis a₁ = 1.778 au and an eccentricity e₁ = 0.475. The red curve represents the separatrix of the system, while the blue curve illustrates the pairs (Ω₂, i₂) that vanish the ω₂ quadrupole precession rate for an inner perturber of e₁ = 0.475. Right panel: temporal evolution of the argument of pericenter ω₂ of the particle.