The analyses of Titan's gravity field obtained by Cassini space mission suggest the presence of an internal ocean beneath its icy surface. The charac…

Radial velocity surveys are now able to detect terrestrial planets at habitable distance from M-type stars. Recently, two planets with minimum masses…

We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining bo…

A statistical analysis is performed over more than 1001 different integrations of the secular equations of the Solar system over 5 Gyr. With this sec…

There are two main reasons why relative equilibria of N point masses under the influence of Newton attraction are mathematically more interesting to …

We describe the first determination of thermal properties and size of the M-type asteroid (16) Psyche from interferometric observations obtained with…

We consider V the potential of the n body problem in the plane

We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree -1 which are invariant by rotation. We…

In the framework of a 30-night spectroscopic survey of small near-Earth asteroids (NEAs) we present new results regarding the identification of olivi…

Context. Ceres is the most massive body of the asteroid belt and contains about 25 wt.% (weight percent) of water. Understanding its thermal evolutio…

We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation ve…

In Noyelles et al. (2008, Astron. Astrophys., 478, 959-970), a resonance involving the wobble of Titan is hinted. This paper studies this scenario an…

Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Po…

Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-…

Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in m…

In his fondamental "Essay on the 3-body problem", Lagrange, well before Jacobi's "reduction of the node", carries out the first complete reduction of…

We prove a meromorphic integrability condition at order 2 near a homothetic orbit for a meromorphic homogeneous potential of degree -1, which extend …

By application of KAM theorem to Lidov-Ziglin's global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish t…

Let V be a meromorphic potential on S. We say that V is homogeneous if there exists such that

We present various properties of algebraic potentials, and then prove that some Morales-Ramis theorems readily apply for such potentials even if they…

It is not so rare that a transcendental function appear in the variational equation. To prove non-integrability, we need to study its Galois group. In general it is possible to avoid it by just taking a particular orbit for which this case does not …

We prove that the motion of a triaxial Riemann ellipsoid of homogeneous liquid without angular momentum does not possess an additional first integral…

We have generalized Theorem 1 of Combot (2011) for any negative homogeneity degree k<0. We could of course ask what happen for positive homogeneity degree. Our result of Theorem 1 still holds, but it is no longer sufficient to make a complete classi…

We prove that the only meromorphically integrable planar homogeneous potential of degree k <> -2,0,2 having a multiple Darboux point is the potential…

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