2005ApJ...628.1006R

The main goal of this work is to analyze the possible dynamical mechanisms that dominate the motion of the HD 12661 extrasolar planetary system. By an analytical approach using the expansion of the disturbing function given by Ellis and Murray, we solve the equation of motion working in a Hamiltonian formulation with the corresponding canonical variables and by means of appropriate canonical transformations. Comparing these results with a direct numerical integration, we can conclude that the system is dominated by a pure secular evolution that is very well reproduced with a disturbing function including at least sixth-order terms in the eccentricities. Because of the uncertainties in the orbital elements of the planets, we also contemplate the occurrence of mean motion resonances in the system and analyze possible contribution from these resonant terms to the total motion.