Poincaré sections of the dynamics driven by both the planetary and galactic perturbations (Hamiltonian from Eq. (13)). The semi-major axis taken as parameter is a = 500 au. The colour scale shows the maximum orbital change rate between two successive points (see titles), and the grey zones are forbidden. Top: section for au²yr⁻² at Ω_G = 0 decreasing. The islands located at e ≈ 0.8 are due to the resonance 2ω + Ω, and the islands located at e ≈ 0.2 are due to librations of ω while I ≈ 63^o (Lidov–Kozai mechanism). Bottom: section for au²yr⁻² at ω_G = 0 decreasing. The chaotic bands are due to the overlap of the resonances ω − Ω and 2ω − Ω (for I < 90^o), or ω + Ω and 2ω + Ω (for I > 90^o), and the islands located at I ≈ 90^o are due to librations of Ω (orthogonal Laplace plane).