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In this paper, we use a semi-analytical approach to analyze the globalstructure of the phase space of the planar planetary 3/1 mean-motion resonance,in cases where the outer planet is more massive than its inner companion. Weshow that the resonant dynamics can be described using only two fundamentalparameters, the total angular momentum and the scaling parameter. The topologyof the Hamiltonian function describing the resonant behaviour is studied on therepresentative planes that allows us to investigate a large domain of the phasespace of the three-body problem without time-expensive numerical integrationsof the equations of motion, and without any restriction on the magnitude of theplanetary eccentricities. The families of the well known Apsidal CorotationResonances (ACR) parameterized by the planetary mass ratio are obtained andtheir stability is analyzed. The main dynamical features in the domains aroundACR are also investigated in detail by means of spectral analysis techniques,which allow us to detect the regions of different regimes of motion of resonantsystems. The construction of dynamical maps for various values of the totalangular momentum shows the evolution of domains of stable motion with theeccentricities, identifying possible configurations suitable for exoplanetarysystems.

Dynamics of the 3/1 planetary mean-motion resonance. An application to the HD60532 b-c planetary system