Related papers: Sums Associated with Orbits in the Binary Dynamica…
There are well-known analogs of the prime number theorem and Mertens' theorem for dynamical systems with hyperbolic behaviour. Here we consider the same question for the simplest non-hyperbolic algebraic systems. The asymptotic behaviour of…
We extend the formalism of a previous paper to include the effects of flybys and instantaneous perturbations such as supernovae on the long-term secular evolution of hierarchical multiple systems with an arbitrary number of bodies and…
The Darwin instability effect in the binary systems (planets, stars, and galaxies) is analyzed within the model based on the Regge-like laws. New analytical formulas are presented for the relative distance between components of the binary…
We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or…
Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10-13, 1983) equations for mirror symmetries among the distances of the planets…
The orbital and eccentricity evolution for compact object binaries through gravitational wave emission first derived by Peters and Mathews are used extensively throughout the gravitational wave community for calculating the orbital…
Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system…
A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product…
Gross and Smith have put forward generalizations of Hardy - Littlewood twin prime conjectures for algebraic number fields. We estimate the behavior of sums of a singular series that arises in these conjectures, up to lower order terms. More…
We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
The full two-body problem (F2BP) is often used to model binary asteroid systems, representing the bodies as two finite mass distributions whose dynamics are influenced by their mutual gravity potential. The emergent behavior of the F2BP is…
Stars are commonly formed in binary systems, which provide a natural laboratory for studying planet formation in extreme conditions. In our first paper (Paper I) of a series Xie et al. (2011), we have shown that the intermediate stage -…
We postulate that most stars are born in aggregates of binary systems which are dynamically equivalent to the `dominant mode cluster'. The initial binary orbits are consitent with pre-main sequence data. Stellar masses are paired at random…
Supermassive black hole binaries may form as a consequence of galaxy mergers. Both prograde and retrograde orbits have been proposed. We study a binary of a small mass ratio, q, in a retrograde orbit immersed in and interacting with a…
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…
Although planets have been found orbiting binary systems, whether they can survive binary interactions is debated. While the tightest-orbit binaries should host the most dynamically stable and long-lived circumbinary planetary systems, they…
A widely considered characteristic of extra-solar planetary systems has been a seeming tendency for major axes of adjacent orbits to librate in stable configurations. Based on a new catalog of extra-solar planets (Butler et al. 2006) and…
Planets have been observed in tight binary systems with separations less than 20 AU. A likely formation scenario for such systems involves a dynamical capture, after which high relative inclinations are likely and may lead to Kozai…
Recently, the spinning tethered system is regarded as a typical and fundamental space structure attracting great interest of the aerospace engineers, and has been discussed primarily for specific space missions in past decades, including…