Proper frequencies of test particles’ motion in the 1:2 MMR on (a, i) plane. From left to right, the panels show the proper frequencies of the resonance angle (f), of perihelion (𝑔), and of ascending node (s), respectively. From top to bottom, test particles have increasing initial eccentricities, from 0.1 to 0.4, as labelled in each panel. The colour indicates the logarithm of the proper frequency in 2π yr⁻¹. The black lines mark the boundary between the horseshoe and asymmetric resonance islands. In between the lines are the asymmetric resonance island. In the blank area, orbits initialised there are unstable and cannot survive the orbital integration of ~34 Myr.