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Fig. 1

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Groups of families, Si (i = 1…6), of planar symmetric periodic orbits in the 1:2:3 resonant chain with stable segments close to the dynamical vicinity of Kepler-51 presented on the (e1, e2) and (e2, e3) planes. Each of these six groups consists of families of the same configuration (shown in Table 3), but with different planetary mass-ratios, that is, (shown in Table 1 and labeled from 1 to 4 on each panel). Label 1 corresponds to Masuda (2014), label 2 to Libby-Roberts et al. (2020), label 3 to default, and label 4 to high-mass priors considered by Battley et al. (2021). The stable (unstable) periodic orbits are depicted by blue (red) solid curves.

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