Topology of the Hamiltonian on different representative planes, (a) The topology on period ratio plane (n₁/n₂, n₂/n₃) with fixed eccentricities. (b) The topology on eccentricity plane (e₁,e₂). The stationary solution located at (n₁/n₂, n₂/n₃) = (2, 1.5) and (e₁, e₂, e₃) = (0.00458, 0.00938, 0.00564) is marked by a red dot on both panels. The corresponding critical angles are (θ₁₂, Δϖ₁₂, θ₂₃, Δϖ₂₃) = (π, 0, π, π). The colour indicates the value of Hamiltonian, light yellow for high and dark blue for low. The same colour code is adopted in all figures in this paper, unless otherwise stated.