Orateur
Description
Since the birth of KAM theory, planetary three-body problems were indicated as a natural benchmark to study its applicability to realistic systems of physical interest. It is well known that KAM statements proved in a purely analytical way completely fail such a challenging purpose. This the reason why, since the last two decades of the previous century Computer-Assisted Proofs (hereafter CAPs)
are commonly used in this context.
We revisit this general problem in the case of a few planar models of extrasolar systems hosting one star and two exoplanets; we consider them with values of the parameters that are in agreement with the observations. The existence of invariant KAM tori in correspondence with orbital motions is investigated by using a publicly available software code, that is specially designed to perform CAPs. Such an approach can be successful if and only if the problem is described by
a Hamiltonian (in action-angle coordinates) that is close enough to a Kolmogorov normal form. We describe the bare minimum of preliminary canonical transformations, which are needed to bring the Hamiltonian in a suitable form to start a CAP. This strategy is implemented in such a way to rigorously prove the existence of KAM tori for three exoplanetary systems (namely HD11964, HD142 and HD4732). A rather simple argument allows us to give a characterization of the planetary systems for which our proof scheme has good chance of success.
This talk is based on a joint work with C. Caracciolo.
