相关论文: A new method for the determination of action integ…
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,…
We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits…
The usefulness of angle-action variables in galaxy dynamics is well known, but their use is limited due to the difficulty of their calculation in realistic galaxy potentials. Here we present a method for estimating angle-action variables in…
A phase-space distribution function of the steady state in galaxy models that admits regular orbits overall in the phase-space can be represented by a function of three action variables. This type of distribution function in Galactic models…
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
We describe a method for calculating action-angle variables in axisymmetric galactic potentials using Birkhoff normalization, a technique from Hamiltonian perturbation theory. An advantageous feature of this method is that it yields…
We present a method for extracting actions, angles and frequencies from an orbit's time series. The method recovers the generating function that maps an analytic phase-space torus to the torus to which the orbit is confined by…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…
The correlation dimension, that is, the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of nonlinear dynamics in order to compute…
Angle-action coordinates are used to study the relic of an N-body simulation of a self-gravitating satellite galaxy that was released on a short-period orbit within the disc of the Galaxy. Satellite stars that lie within 1.5 kpc of the Sun…
Two motions in the galactic plane have been detected and characterized, based on the determination of a common systematic component in Hipparcos catalogue proper motions. The procedure is based only on positions, proper motions and…
Most measurements of mass in Astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of underlying…
A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…
A trivial bundle of regular connected invariant manifolds of a completely integrable Hamiltonian system can be provided with action-angle coordinates.
A time-dependent completely integrable Hamiltonian system is proved to admit the action-angle coordinates around any regular instantly compact invariant manifold. Written relative to these coordinates, its Hamiltonian and first integrals…
We use the action-angle variables to describe the geodesic motions in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to study thoroughly the complete integrability of the system. We find that the…
We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie…
The transformation from angle-action variables to Cartesian coordinates is a crucial step of the (semi) classical description of bimolecular collisions and photo-fragmentations. The basic reason is that dynamical conditions corresponding to…
A new dynamical parameter, the f-indicator, is introduced and used in order to distinguish between regular and chaotic motion in galactic Hamiltonian systems. Two kinds of galactic potentials are used: (i) a global potential, which…
We present an approach to the design of distribution functions that depend on the phase-space coordinates through the action integrals. The approach makes it easy to construct a dynamical model of a given stellar component. We illustrate…