2:1 resonance energy levels in section planes defined by: e₂ = 0 (top left), cosσ₁ = cosσ₂ = 0 (top right), sinσ₁ = sinσ₂ = 0 (bottom left), and e₁ = 0 (bottom right). Stable ACR solutions are highlighted with colored dots (red and green). Unstable ones are highlighted with colored crosses (blue). The star mass is given by m₀ = m_⊙ and planets masses by m₁ = m₂ = m _⊕ . The constant G is set to G = G₀(1−10^-4). The Hamiltonian is developed up to degree 4-1.