相关论文: On the "Blue sky catastrophe termination" in the r…

The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…

The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family…

We present a global analysis of the center manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1…

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…

We present a numerical study on the stability of all fourth- and fifth-order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, and 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet, and an additional…

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…

A unified framework is proposed to quantitatively characterize pitchfork bifurcations and associated symmetry breaking in the elliptic restricted three-body problem (ERTBP). It is known that planar/vertical Lyapunov orbits and Lissajous…

We consider the Hill four-body problem where three oblate, massive bodies form a relative equilibrium triangular configuration, and the fourth, infinitesimal body orbits in a neighborhood of the smallest of the three massive bodies. We…

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admit certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection --…

Consider n=2l>=4 point particles with equal masses in space, subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group D_l, where D_l is the group of order 2l generated by two rotations of angle…

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…

The geometry of the weak stability boundary region for the planar restricted three-body problem about the secondary mass point has been an open problem. Previous studies have conjectured that it may have a fractal structure. In this paper,…

We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the…

The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem…

We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very…

Consider four point particles with equal masses in the euclidean space, subject to the following symmetry constraint: at each instant they are symmetric with respect to the dihedral group $D_2$, that is the group generated by two rotations…

Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…

We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L2 up to half the distance to the smaller primary in the Jupiter-Sun planar restricted circular three body problem. We then focus on a…

We analyze the asymptotic behaviour of the coupled cluster many-body wave-function in the limit of highly excited two- and three-particles states. We find that in this limit the different coupled cluster amplitudes exhibit a recurring…