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It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
A 3D dynamical model with a quasi-homogeneous core and a disk component is used for the chaos control in the central parts of elliptical galaxy. Numerical experiments in the 2D system show a very complicated phase plane with a large chaotic…
The structure and kinematics of the recognized stellar components of the Milky Way are explored, based on well-determined atmospheric parameters and kinematic quantities for 32360 calibration stars from the Sloan Digital Sky Survey (SDSS)…
The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no longer a canonical Hamiltonian system so that the construction…
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…
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function $H$ and a Casimir $C$ of the corresponding Lie algebra. The orbits of the system are included in…
An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…
The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. We develop a data-analysis pipeline based on the time-distance helioseismology method to…
The hierarchical structure formation model predicts that stellar halos should form, at least partly, via mergers. If this was a predominant formation channel for the Milky Way's halo, imprints of this merger history in the form of moving…
We study maps on the set of permutations of n generated by the R\'enyi-Foata map intertwined with other dihedral symmetries (of a permutation considered as a 0-1 matrix). Iterating these maps leads to dynamical systems that in some cases…
A class of Hamiltonian stochastic differential equations with multiplicative L\'{e}vy noise in the sense of Marcus, and the construction and numerical implementation methods of symplectic Euler scheme, are considered. A general symplectic…
We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase…
Resolved surveys of the Milky Way's stellar halo can obtain all 6 phase space coordinates of tens of thousands of individual stars, making it possible to compute their 3-dimensional orbits. Spectral analysis of large numbers of halo orbits…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to…
The Galactic disk is expected to be spatially, kinematically, and chemically clustered on many scales due to both star formation and non-axisymmetries in the Galactic potential. In this work we calculate the spatial and kinematic two-point…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
The main objective of this work is to determine the character of orbits of stars moving in the meridional $(R,z)$ plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical…