Abstract

The study of exoplanetary systems with two or more planets in orbits with non-zero mutual inclination is an interesting topic of Hamiltonian dynamics, in view of the many applications related to the astronomical discovery, in the last 20 years, of several such systems.

The present report discusses the mathematical context of the theory of the long term stability for nearly Keplerian perturbed n-body systems, following the so-called Kolmogorov-Arnold-Moser (KAM) Theorem. The KAM Theorem is a cornerstone of canonical perturbation theory: it allows to conjugate, through a convergent sequence of canonical trasformations, particular solutions of the “pertubed” dynamical system to the invariant dynamics on a torus. We provide a short summary of classical results of perturbation theory. We also briefly present some recent progress on the construction of the Kolmogorov normal form for “isochronous systems”. Finally, we explain in an introductory manner, how the above concepts can be implemented in exoplanetary systems with a 3D-orbital architecture.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.