Related papers: A numerical criterion evaluating the robustness of…
We study the planetary system of $\upsilon$~Andromed{\ae}, considering the three-body problem formed by the central star and the two largest planets, $\upsilon$~And~\emph{c} and $\upsilon$~And~\emph{d}. We adopt a secular, three-dimensional…
We reconsider the problem of the orbital dynamics of the innermost exoplanet of the $\upsilon$-Andromedae system (i.e., $\upsilon$-And $\mathbf{b}$) into the framework of a Secular Quasi-Periodic Restricted Hamiltonian model. This means…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in…
The large increase in exoplanet discoveries in the last two decades showed a variety of systems whose stability is not clear. In this work we chose the $\upsilon$ Andromedae system as the basis of our studies in dynamical stability. This…
The Upsilon Andromedae system is the first exoplanetary system to have the relative inclination of two planets' orbital planes directly measured, and therefore offers our first window into the 3-dimensional configurations of planetary…
Because of the high eccentricities (~0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital…
We present results of extensive numerical studies of the stability of non-interacting particles in the planetary systems of stars Upsilon Andromedae, GJ 876, 47 UMa, and 55 Cancri. We discuss the possibility of the existence of islands of…
We study the dynamics of the upsilon-Andromedae planetary system proposed by Curiel et al. (2011). We focus on the study of the 3:1 Mean Motion Resonance between upsilon-Andromedae-d and the recently discovered upsilon-Andromedae-e…
We review the orbital dynamics exhibited by the first extra-solar planetary system discovered, Upsilon Andromedae. This system is unique in combining all of the surprising architectural features displayed individually by extrasolar…
(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…
We present theoretical analysis of the astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). Particularly, we derive a model for the future measurements with SIM and discuss the problem of reliable…
We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of application for systems with 2 and 3 degrees of freedom. The first…
In this paper we discuss about the possibility of {\it coexistence} of stable and unstable quasi--periodic {\sc kam} tori in a region of phase space of the three-body problem. The {argument of proof} goes along {{\sc kam} theory and,…
We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in (Laskar, PRL,2000). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome…
The bright F8 V solar-type star upsilon Andromedae has recently been reported to have a system of three planets of Jovian masses. In order to investigate the orbital stability and mutual gravitational interactions among these extrasolar…
It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…
The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability of the system. Focusing on the…
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are…
Our understanding of the mechanisms governing the structure and secular evolution galaxies assume nearly integrable Hamiltonians with regular orbits; our perturbation theories are founded on the averaging theorem for isolated resonances. On…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems.…