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Fig. 2

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Energy levels sections in the plane defined by sinσ1 = sinσ2 = 0 for the 2:1 resonance (A1 to F1), and the 3:2 resonance (A2 to F2). The constant G/G0 − 1 is set to −10-3 (A1, A2), −5 × 10-4 (B1, B2), −10-4 (C1, C2), −3.2 × 10-5 (D1, D2), −3 × 10-5 (E1, E2), and  + 10-3 (F1, F2). 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 Hamiltonian is developed up to degree 4-1. Note that the scales are different for graphs A1, A2, B1, and B2 than for other graphs.

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