Related papers: Regions without invariant tori of given class for …
The conefield variant of a Converse KAM method for 3D vector fields, identifying regions through which no invariant 2-tori pass transverse to a specified direction field, is tested on some helical perturbations of an axisymmetric magnetic…
A Converse KAM method for 3D vector fields, establishing regions through which pass no invariant 2-tori transverse to a given direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry.…
This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Near the Lagrangian equilibrium $\mathcal{L}_4$ a twistless…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the…
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…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We carried out an…
In this paper, we study the Birkhoff sections in a 3-manifold foliated by invariant tori. We establish the necessary and sufficient conditions for various types of periodic orbits to serve as boundary orbits of a Birkhoff section. The…
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…
We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2,…
We consider a symmetric five-body problem with three unequal collinear masses on the axis of symmetry. The remaining two masses are symmetrically placed on both sides of the axis of symmetry. Regions of possible central configurations are…
The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading…
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to…
We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are…
We consider the problem of the determination of the isotropy classes of the orbit spaces of all the real linear groups, with three independent basic invariants satisfying only one independent relation. The results are obtained in the $\hat…