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A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
A test particle in a noncoplanar orbit about a member of a binary system can undergo Kozai-Lidov oscillations in which tilt and eccentricity are exchanged. An initially circular highly inclined particle orbit can reach high eccentricity. We…
Globular clusters rotate significantly, and with the increasing amount of detailed morphologicaland kinematical data obtained in recent years on galactic globular clusters many interesting features show up. We show how our theoretical…
The study of off-equatorial orbits in razor-thin disks is still in its beginnings. Contrary to what was presented in the literature in recent publications, the vertical stability criterion for equatorial circular orbits cannot be based on…
The stellar velocity fields of elliptical galaxies hold clues to their dynamical structure and origin. The construction of velocity field models is greatly simplified by assuming an approximate geometrical form for the streamlines of the…
We study circular orbits that are tilted with respect to the equatorial plane around a Kerr black hole. We write the equations for the parameters of a tilted circular orbit in terms of the orbit's radius and the Carter constant, or…
Galactic disks lie at the heart of many of the most pressing astrophysical puzzles. There are sophisticated kinetic theories that describe some aspects of galaxy disk dynamics, but extracting quantitative predictions from those theories has…
Most extrasolar planets currently known were discovered by means of an indirect method that measures the stellar wobble caused by the planet. We previously studied a triple system composed of a star and a nearby binary on circular coplanar…
We simulate the observations of proper motion of stars very close to the Galactic Center. We show that the speckle interferometry done with the Keck II telescope is accurate enough to obtain orbital parameters for stars with the period P…
We have calculated the non-radial oscillation in slowly rotating relativistic stars with the Cowling approximation. The frequencies are compared with those based on the complete linearized equations of general relativity. It is found that…
A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…
Stationary stellar systems with radially elongated orbits are subject to radial orbit instability -- an important phenomenon that structures galaxies. Antonov (1973) presented a formal proof of the instability for spherical systems in the…
We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent,…
A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one.…
Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…
We calculate stationary configurations of rapidly rotating compact stars in general relativity, to study the properties of circular orbits of test particles in the equatorial plane. We search for simple, but precise, analytical formulae for…