We study the relative equilibria of the limit case of the pla- nar Newtonian 4{body problem when three masses tend to zero, the so-called (1 + 3){body problem. Depending on the values of the in- nitesimal masses the ...

In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy ...

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the ...

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the ...

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a ...

We prove the existence of infinitely many symmetric periodic orbits for a regularized rhomboidal five-body problem with four small masses placed at the vertices of a rhombus centered in the fifth mass. The main tool for ...

We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of ...

In this paper we prove the existence of central configurations of the pnbody problem where the masses are at the vertices of p nested regular n-gons with a common center for all p ≥ 2 and n ≥ 2. In such configurations ...

We analytically study the Hamiltonian system in R4 with Hamiltonian H = 1 2 p2 x +p2 y + 1 2 ω2 1x2 +ω2 2y2 − εV (x, y) being V (x, y) = −(x2y + ax3) with a ∈ R, where ε is a small parameter and ω1 and ω2 ...