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We study the establishment of three-planet resonances -similar to the Laplaceresonance in the Galilean satellites- and their effects on the mutualinclinations of the orbital planes of the planets, assuming that the latterundergo migration in a gaseous disc. In particular, we examine the resonancerelations that occur, by varying the physical and initial orbital parameters ofthe planets (mass, initial semi-major axis and eccentricity) as well as theparameters of the migration forces (migration rate and eccentricity dampingrate), which are modeled here through a simplified analytic prescription. Wefind that, in general, for planetary masses below 1.5 M_J, multiple-planetresonances of the form n3:n2:n1=1:2:4 and 1:3:6 are established, as the innerplanets, m1 and m2, get trapped in a 1:2 resonance and the outer planet m3subsequently is captured in a 1:2 or 1:3 resonance with m2. For mildeccentricity damping, the resonance pumps the eccentricities of all planets ona relatively short time-scale, to the point where they enter aninclination-type resonance (as in Libert & Tsiganis 2011); then mutualinclinations can grow to ~35{\deg}, thus forming a "3-D system". On the otherhand, we find that trapping of m2 in a 2:3 resonance with m1 occurs veryrarely, for the range of masses used here, so only two cases of capture in arespective three-planet resonance were found. Our results suggest that trappingin a three-planet resonance can be common in exoplanetary systems, providedthat the planets are not very massive. Inclination pumping could then occurrelatively fast, provided that eccentricity damping is not very efficient sothat at least one of the inner planets acquires an orbital eccentricity higherthan e=0.3.

Trapping in three-planet resonances during gas-driven migration