Related papers: On the $ C^{8/3} $-Regularisation of Simultaneous …
We discuss a model providing two different stationary background solutions with flat and $dS_{4}$ metric on the branes under the same values of the fundamental parameters. It is shown that only an additional fine-tuning of the brane scalar…
We follow the sinking of two massive black holes in a spherical stellar system where the black holes become bound under the influence of dynamical friction. Once bound, the binary hardens by three-body encounters with surrounding stars. We…
Binary-star exoplanetary systems are now known to be common, for both wide and close binaries. However, their orbital evolution is generally unsolvable. Special cases of the N-body problem which are in fact completely solvable include…
The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four body problem. The problem can be viewed as a two parameter family of conservative autonomous vector fields. The main tools are…
In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the eight figure choreography, and we explore some symmetric periodic orbits of…
For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
Modern cyber-physical systems (CPS) integrate physics, computation, and learning, demanding modeling frameworks that are simultaneously composable, learnable, and verifiable. Yet existing approaches treat these goals in isolation: causal…
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is…
The degeneracy of central configurations in the planar $N$-body problem makes their enumeration problem hard and the related dynamics appealing. To truly understand the bifurcations of central configurations, we should work in the FULL…
For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…
In this paper we investigate the problem of linearizability for a family of cubic complex planar systems of ordinary differential equations. We give a classification of linearizable systems in the family obtaining conditions for…
The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the…
In this paper, we study a model of simplified four-body problem called planar two-center-two-body problem. In the plane, we have two fixed centers $Q_1=(-\chi,0)$, $Q_2=(0,0)$ of masses 1, and two moving bodies $Q_3$ and $Q_4$ of masses…
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
We provide an upper bound for the number of limit cycles that planar polynomial differential systems of a given degree may have. The bound turns out to be a polynomial of degree four in the degree of the system. The strategy brings together…
In this paper, we describe a gradient-free method to solve a system of equations, and we use it to construct two families of pseudo-periodic planar solutions of the 4- and 6-body problem. The method is a stochastic black-box procedure that…