Related papers: Comet and moon solutions in the time-dependent res…

In this talk I describe recent joint works with R.Schoen and with G.Gibbons and R.Schoen which prove the non-existence of certain asymptotically flat, stationary solutions of the Einstein equations with more than one body. The basic…

We prove the existence of relative periodic solutions of the planar $N=\sum_{j=1}^n k_j$-body problem starting with $n$ bodies moving close to a non-degenerate central configuration and replacing each of them with clusters of $k_j$ bodies…

Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a…

We consider the $N$-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of locked inertia tensor, we compute the moment of inertia for systems moving on spheres and hyperbolic spheres and show that…

Consider the time-periodic flow of an incompressible viscous fluid past a body performing a rigid motion with non-zero translational and rotational velocity. We introduce a framework of homogeneous Sobolev spaces that renders the resolvent…

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…

We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…

Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…

We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…

In the Newtonian $n$-body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic results about their Morse and Maslov indices. Moreover for…

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on…

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at…

In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically…

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 the existence of a number of smooth periodic motions $u_*$ of the classical Newtonian $N$-body problem which, up to a relabeling of the $N$ particles, are invariant under the rotation group ${\cal R}$ of one of the five Platonic…

Central configurations are fundamental equilibrium solutions of the Newtonian $n$-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such…

The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…

In this paper, we continue our analysis of the chaotic four-body problem by presenting a general ansatz-based analytic treatment using statistical mechanics, where each outcome of the four-body problem is regarded as some variation of the…

We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…

The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…