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The dynamics of systems of two and three planets, initially placed oncircular and nearly coplanar orbits, is explored in the proximity of theirstability limit. The evolution of a large number of systems is numericallycomputed and their dynamical behaviour is investigated with the frequency mapanalysis as chaos indicator. Following the guidance of this analysis, it isfound that for two-planet systems the dependence of the Hill limit on theplanet mass, usually made explicit through the Hill's radius parametrization,does not appear to be fully adequate. In addition, frequent cases of stablechaos are found in the proximity of the Hill limit. For three-planet systems,the usual approach adopted in numerical explorations of their stability, wherethe planets are initially separated by multiples of the mutual Hill radius,appears too reducing. A detailed sampling of the parameter space reveals thatsystems with more packed inner planets are stable well within previousestimates of the stability limit. This suggests that a two-dimensional approachis needed to outline when three-planet systems are dynamically stable.

Dynamical behaviour of multiplanet systems close to their stability limit