相关论文: Perihelia reduction and global Kolmogorov tori in …

We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of $(3n-2)$--dimensional quasi--periodic motions in the spacial, planetary $(1+n)$--body problem away from…

We prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic…

The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the…

We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which…

Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \[ H_\epsilon (\varphi,I,t)=H_0(I)+\epsilon H_1(\varphi,I,t), \varphi\in T^2,\ I\in U\subset R^2,\ t\in…

Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…

By introducing a new coordinate system, we prove that there are abundant new periodic orbits near relative equilibrium solutions of the N-body problem. We consider only Lagrange relative equilibrium of the three-body problem and…

For any subcritical index of regularity $s>3/2$, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space…

The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…

Since the strong degeneracies present in the N-body problem, even in the basic case of the planar three-body problem, nobody inspects the problem of nonlinear stability of Lagrange relative equilibrium. We introduce a new coordinate system…

We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic…

We consider the vacuum Einstein field equations under the Belinski-Zakharov symmetry, which leaves the problem as a 1+1-dimensional quasilinear system of PDEs. Depending on the chosen signature of the metric, these spacetimes contain most…

A normal form theory for non--quasi--periodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in [15] to prove, in the averaged, planar three--body problem, the existence of a plenty…

The KAM (Kolmogorov-Arnold-Moser) theorem guarantees the stability of quasi-periodic invariant tori by perturbation in some Hamiltonian systems. Michel Herman proved a similar result for quasi-periodic motions, with $k$-dimensional…

The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained…

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…

A family of polynomial coupled function of $n$ degree is proposed, in order to generalize the Levi-Civita regularization method, in the restricted three-body problem. Analytical relationship between polar radii in the physical plane and in…

We use the corrections to the Newton-Einstein secular precessions of the longitudes of perihelia of some planets (Mercury, Earth, Mars, Jupiter, Saturn) of the Solar System, phenomenologically estimated as solve-for parameters by the…

A gravitational close encounter of a small body with a planet may produce a substantial change of its orbital parameters which can be studied using the circular restricted three-body problem. In this paper we provide parametric…

Most attempts to unify general relativity with the standard model of particle physics predict violations of the equivalence principle associated in some way with the composition of the test masses. We test this idea by using observational…