Dynamical maps of the domain around the stable symmetric ACRs with e₁ = 0.03 (top left) and 0.05 (top right); and, e₁ = 0.067 (bottom left) and 0.08 (bottom right) with m₂/m₁ = 0.45. The light tones correspond to stable motions, while the increasingly dark tones correspond to increasingly chaotic motions. The dark-blue regions correspond to initial conditions for which no solutions exist for the fixed values of the angular momentum and the scaling parameter. Finally, the domains of initial conditions leading to the collision/ejection of the planets within 3 Myr are light-blue colored. The initial value of σ₁ is fixed at 0 and the initial value of Δϖ is fixed at 0 (positive values on the e₂-axis) or 180° (negative values on the e₂-axis). The red cross in the bottom left plane shows the location of the HD 200964 system simulated in Sect. 3.