The three typical phase spaces of the simplified model (Hamiltonian (49)) for a second-order resonance. We plot the energy levels in the complex plane (real and imaginary parts of u₁), for R = 0.1 and δ = −0.2 (top), 0 (middle), 0.2 (bottom). Elliptical (stable) fixed points are marked with dots, while hyperbolic (unstable) ones are marked with crosses. R corresponds to a resonant area and C_e (respectively C_i) to external (respectively internal) circulation.