TITLE: Stability of non-coplanar extrasolar systems
SPEAKER: Dr. Mara Volpi (Dep. of Mathematics, University of Rome Tor Vergata)
ABSTRACT: Due to the limitations of the radial velocity method, our
knowledge of the spatial configuration of the hundreds of exoplanetary
systems discovered so far is limited. Through an analytical study
based on a secular Hamiltonian expansion and numerical explorations
performed with a chaos detector, our aim is to provide constraints on
the orbital inclinations and the mutual inclinations of several
two-planet extrasolar systems, that ensure the long-term stability of
the system. The work presented is two-fold. On the one hand, we rely
on perturbation theory and apply a reverse KAM approach to determine
the ranges of the mutual inclination that allow the convergence of the
algorithm constructing the invariant tori. On the other hand, we
perform a parametric study via numerical integrations to find
long-term stable non-coplanar configurations, focusing on the
existence of the Lidov-Kozai resonance. We also show how the
relativistic effects influence the extent of the Lidov-Kozai resonant
region for planetary systems with close-in planets.
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