Related papers: Orbit Determination with the two-body Integrals. I…
The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability…
We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular…
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
We give a generalization to higher dimensions of Silverman's result on finiteness of integer points in orbits. Assuming Vojta's conjecture, we prove a sufficient condition for morphisms on P^N so that (S,D)-integral points in each orbit are…
Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…
A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem…
We report on the preliminary determination of the visual orbit of the double-lined spectroscopic binary system BY Draconis with data obtained by the Palomar Testbed Interferometer in 1999. BY Dra is a nearly equal-mass double-lined binary…
We introduce analysis of orbital parities as a concept and a tool for understanding radicals. Based on fundamental reduced one- and two-electron density matrices, our approach allows us to evaluate a total measure of radical character and…
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 demonstrate how measuring orbital period derivatives can lead to more accurate distance estimates and transverse velocities for some nearby binary pulsars. In many cases this method will estimate distances more accurately than is…
We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for…
We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in…
A new analytical approach to the motion and radiation of (comparable mass) binary systems has been introduced in 1999 under the name of Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of…
We use post-Newtonian (PN) approximations to determine the initial orbital and spin parameters of black hole binaries that lead to low-eccentricity inspirals when evolved with numerical relativity techniques. In particular, we seek initial…
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.