Related papers: Quasi-periodic Almost-collision Orbits in the Spat…
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…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
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 treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…
In this article we continue the study of the collapse of three inelastic particles in dimension $d \geq 2$, complementing the results we obtained in its companion paper. We focus on the particular case of the nearly-linear inelastic…
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
At the Lagrange relative equilibrium of the three-body problem, for all values of the masses, the elliptic eigenvalues associated with vertical eigenvectors give rise to spatial quasi-periodic orbits, which become periodic in a rotating…
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
Li and Liao announced (2019) discovery of 313 periodic collisionless orbits' initial conditions (i.c.s), 30 of which have equal masses, and 18 of these 30 orbits have physical periods (scale-invariant periods) $T^{*}=T|E|^{3/2}<80$. That…
A very few three-dimensional (3D) periodic orbits of general three-body problem (with three finite masses) have been discovered since Newton mentioned it in 1680s. Using a high-accuracy numerical strategy we discovered 10,059…
The rotation of asymmetric bodies in eccentric Keplerian orbits can be chaotic when there is some overlap of spin-orbit resonances. Here we show that the rotation of two coorbital bodies (two planets orbiting a star or two satellites of a…
The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
In this article we introduce the notion of a k-almost-quasifibration and give many examples. We also show that a large class of these examples are not quasifibrations. As a consequence, supporting the Asphericity conjecture of [19], we…
We perform N-body simulations of young triple systems consisting of two low-mass companions orbiting around a significantly more massive primary. We find that, when the orbits of the companions are coplanar and not too widely separated, the…
We show that the bound states in a three-body system display a Coulomb series with a Gaussian cut-off provided: (i) the system consists of a light particle and two heavy bosonic ones, (ii) the heavy-light short-range potential has a…