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Migration of planetary systems caused by the action of dissipative forces maylead the planets to be trapped in a resonance. In this work we study theconditions and the dynamics of such resonant trapping. Particularly, we areinterested in finding out whether resonant capture ends up in a long-termstable planetary configuration. For two planet systems we associate theevolution of migration with the existence of families of periodic orbits in thephase space of the three-body problem. The family of circular periodic orbitsexhibits a gap at the 2:1 resonance and an instability and bifurcation at the3:1 resonance. These properties explain the high probability of 2:1 and 3:1resonant capture at low eccentricities. Furthermore, we study the resonantcapture of three-planet systems. We show that such a resonant capture ispossible and can occur under particular conditions. Then, from the migrationpath of the system, stable three-planet configurations, either symmetric orasymmetric, can be determined.

Resonant capture of multiple planet systems under dissipation and stable orbital configurations