Analysis of the long-term stability of multi-planetary extrasolar systems and implications on their orbital characteristics

To date, more than 400 multiple extrasolar systems have been discovered.
Due to the limitations of the detection methods, our knowledge of these
systems is imperfect. Using dynamical tools, we aim to better constrain their
physical and orbital parameters. In particular, we will focus on the analysis
of the massive planetary systems discovered with the radial velocity
technique, for which the inclinations of the orbital planes (and thus their
mutual inclinations and planetary masses) are unknown. Investigating the
stability of such systems will be similar to what concerns our Solar system,
where its kernel (made by the Sun, Jupiter and Saturn) is so robust that
stability into the light of KAM theorem is verified. This research project has
the ambition to reverse the usual approach about the possible applications
of KAM theory in Celestial Mechanics, in order to have a better
understanding of the dynamics in multi-planetary extrasolar systems.
Instead of applying the KAM theory to well constrained simplified models of
our Solar system, we will assume that the known extrasolar systems are
stable in KAM sense and deduce the range of values of both inclinations
and masses which are compatible with their stability. The determination of
the inclinations of extrasolar systems is of the highest importance for
formation theories of planetary systems. The first milestone of this work will
be dedicated to secular two-planet systems, while different kinds of systems
will be treated as possible refinements of our model, namely Kozai-resonant
systems, mean-motion resonant systems and systems with more than two
planets.