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We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the…
Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite…
The richness of dynamical behavior exhibited by the rotational states of various solar system objects has driven significant advances in the theoretical understanding of their evolutionary histories. An important factor that determines…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
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…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant,…
This paper presents a study of the Poincar\'e-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant…
Capture in mean motion resonance has been observed in the Solar System for small objects with prograde as well as retrograde orbits of moderate inclinations. However, no example of an object with a nearly polar orbit was known to be in…
Secular resonances in exoplanet systems occur when two or more planets have commensurabilities in the precession rates of their orbital elements, causing an exchange of angular momentum between them. The stellar gravitational quadrupole…
The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is…
Three-body and n-body problems in celestial mechanics are age-old and challenging puzzles. In recent years, several breakthroughs are made in finding periodic orbits for three-body problem. And Bohua Sun proposed a conjecture on Kepler's…
Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that…
Phenomenological rules that govern the collective behaviour of complex physical systems are powerful tools because they can make concrete predictions about their universality class based on generic considerations, such as symmetries,…
The existence of Planet Nine has been suggested to explain the pericenter clustering of extreme trans-Neptunian objects (TNOs). However, the underlying dynamics involving Planet Nine, test particles and Neptune is rich, and it remains…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
We study the gravitational wave emission of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner Hamiltonian formulation, where we include (for the first time in this context) terms up…
Gravitational amplification of Poisson noise in stellar systems increases the dipole noise power by roughly a factor of six and the quadrupole noise by 50% for a King model profile. The dipole noise is amplified by a factor of fifteen for…
Motivated by the recently obtained HAL QCD potentials for the $N$-$\phi$, $N$-$J/\psi$, and $N$-$\eta_c$ interactions, we investigate the structure of the exotic nuclei $^{8}_{\phi}{\text{Be}}$, $^{8}_{J/\psi}{\text{Be}}$, and…
We consider a hierarchical triple system consisting of an inner eccentric binary with an outer companion. A highly misaligned circumbinary disk around the inner binary is subject to two competing effects: (i) nodal precession about the…
The pulsar triple system, J0337+1715, is remarkably regular and highly hierarchical. Secular dynamics controls its long term evolution with orbital commensurability having negligible effect. Secular interactions transfer angular momentum…