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Abstract We study the KAM-stability of several single star two-planet nonresonant extrasolar systems. It is likely that the observed exoplanets are the most massive of the system considered. Therefore, their robust stability is a crucial and necessary condition for the long-term survival of the system when considering potential additional exoplanets yet to be seen. Our study is based on the construction of a combination of lower-dimensional elliptic and KAM tori, so as to better approximate the dynamics in the framework of accurate secular models. For each extrasolar system, we explore the parameter space of both inclinations: the one with respect to the line of sight and the mutual inclination between the planets. Our approach shows that remarkable inclinations, resulting in three-dimensional architectures that are far from being coplanar, can be compatible with the KAM stability of the system. We find that the highest values of the mutual inclinations are comparable to those of the few systems for which the said inclinations are determined by the observations.
Caracciolo et al. (Thu,) studied this question.