The mean-motion resonance is one of the most interesting phenomena in celestial mechanics. Its importance lies on the comprehension of the formation and long-term stability of planetary systems in close orbits. In this presentation we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance, in the cases where the outer planet is more massive than its inner companion. By using numerical techniques we are able to find the Apsidal Corotation Resonances (ACR) parametrized by the mass ratio, and to determine its stability. The main dynamical features in the domains around the ACR are also investigated in detail by means of spectral analysis techniques, which allowed us to detect the regions of different regimes of motion of resonance systems. We show the evolution of the dynamical maps constructed for several values of the angular momenta, and identify the possible configurations suitable for exoplanetary systems.
This seminar is supported by Portuguese Funds through the CIDMA - Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ("FCT" - Fundação para a Ciência e a Tecnologia), within the project UID/MAT/04106/2013.