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Fig. 5.

image

Dynamical spectra of icosΩ (top panel), ecosϖ (middle panel), and cosσ (bottom panel). The five most significant frequencies of the highest peaks in the power spectra, which are denoted by red open circles, black open inverted triangles, squares, triangles, and diamonds respectively, are plotted against their initial inclinations (top two panels) or semi-major axes (bottom panel). The proper frequencies which vary continuously with the initial semi-major axis and inclination are indicated by arrows. The initial semi-major axis for orbits in the top two panels is 19.22 AU while the initial inclination for orbits in the bottom panel is 4°. The dashed lines indicate the forced frequencies which are identified to be involved with the frequency of the quasi 1:2 MMR between Uranus and Neptune f2 : 1 or the fundamental frequencies in the outer solar system. In the bottom panel the frequencies 2f, 2f − f2 : 1, and f2 : 1 − f are also labelled. The precession rates of the ascending node for orbits in the top panel, along with s7, are all negative. Hence, the absolute values of these frequencies are plotted.

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