Kepler and K2 systems dynamically unveiled via periodic orbits

Many exoplanetary systems have been discovered so far possessing planets in mean-motion resonances or resonant chains. To tackle the limitations of the observational methods, we resort to the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, which acts as a guide for the validation of the orbital parameters of the detected exoplanets. Additional validations or constraints on the orbital elements are achieved for several two-planet near-resonant systems. In particular, we find that a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, whereas Kepler-9 system can not display such a resonant evolution. For the (non-coplanar) Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance.