Christos Efthymiopoulos

Dipartimento di Matematica “Tullio Levi-Civita”, Universit√† degli Studi di Padova

3D secular dynamics for extrasolar planetary systems: an overview

While averaged models of the planar (2D) planetary 3-body problem yield an integrable dynamics, 3D averaged models yield a rich-in-structure problem associated with a non-integrable two DOF secular Hamiltonian model. The talk will review some basic results stemming from the analysis of such a 3D secular model for exoplanetary dynamics. The emphasis will be on results obtained by a suitable decomposition of the (Jacobi-reduced) Hamiltonian under the form H = Hplanar+ H3D. The term H_planar yields the usual dynamics structured by the nonlinear normal modes associated with apsidal corotation resonances (ACR). The term H3D, instead, leads to a sequence of bifurcations of new periodic orbits which bridge the ACR family with the family of highly inclined circular orbits associated with the Kozai resonance. The talk will review how the structure of the phase space varies by altering a properly chosen parameter (representing, essentially, the increase in mutual inclination), as well as the dependence of phase portraits on the remaining important parameters of the problem, namely the mass ratios of the two planets with respect to the central star and the semi-major axis ratio of the planetary heliocentric orbits (work in collaboration with Rita Mastroianni, UniPD).

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3D secular dynamics for extrasolar planetary systems: an overview
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