相关论文: Approximating Stellar Orbits: Improving on Epicycl…

We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…

It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of…

We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

The alignment of planetary orbits with respect to the stellar rotation preserves information on their dynamical histories. Measuring this angle for young planets help illuminate the mechanisms that create misaligned orbits for older…

The secular approximation of the hierarchical three body systems has been proven to be very useful in addressing many astrophysical systems, from planets, stars to black holes. In such a system two objects are on a tight orbit, and the…

Hundreds of substellar companions to solar-type stars will be discovered with the Kepler satellite. Kepler's extreme photometric precision gives access to low-amplitude stellar variability contributed by a variety of physical processes. We…

Adiabatic modeling of solar-like oscillations cannot exceed a certain level of precision for fitting individual frequencies. This is known as the problem of near surface effects on the mode physics. We present a theoretical study which…

The Galaxy's stellar halo seems to be a tangle of disrupted systems that have been tidally stretched out into streams. Each stream approximately delineates an orbit in the Galactic force-field. In the first paper in this series we showed…

Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies…

A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by…

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…

This work introduces a new fitting formalism for isophotes which enables more accurate modelling of galaxies with non-elliptical shapes, such as disk galaxies viewed edge-on or galaxies with X-shaped/peanut bulges. Within this scheme, the…

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…

In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation…

It is generally assumed that gas in a galactic disk follows closely non self-intersecting periodic stellar orbits. In order to test this common assumption, we have performed MHD simulations of a galactic-like disk under the influence of a…

Working notes on setting up approximate dynamical systems and nonlinear eigenvalue problems, here embedded within the theory of complex nonlinear dynamics. Computations parallel those of linear quantum theory except that we use functional…

The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…

In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…

The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic…