Phase portraits of the system in the plane (ρ,ψ) for different powers n, obtained in terms of the level curves of γ_n (with, in particular, γ₂ = −ln ρ₀). Trajectories of type T₁, T₂, and T₃ are plotted respectively in red, green, and blue. The thick black curve represents the unit level (separatrix). Along it lie the homoclinic orbit and the two branches of the orbit, whereas the circular trajectory T^⋆ is plotted in orange. The white level curve represents the zero level. For n > 2, it always remains in the ρsinψ < 0 side.