Related papers: Order and chaos in galactic maps
We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion…
We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in…
As a first step towards a comprehensive investigation of stellar motions within globular clusters, we present here the results of a study of stellar orbits in a mildly triaxial globular cluster that follows a circular orbit inside a galaxy.…
The regular and chaotic character of orbits is investigated in a 3D potential describing motion in the central parts of a barred galaxy. This potential is an extension in the 3D space of a 2D potential based on a family of figure-eight…
Here I review recent work, by other authors and by myself, on some particular topics related to the regular and chaotic motion in elliptical galaxies. I show that it is quite possible to build highly stable triaxial stellar systems that…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
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…
A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the…
We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
The primary focus of this thesis is the numerical investigation of chaos in Hamiltonian models describing charged particle orbits in plasma, star motions in barred galaxies, and orbits' diffusion in multidimensional maps. We systematically…
Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was…
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 study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron…
We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
Three types of orbits are theoretically possible in autonomous Hamiltonian systems with three degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides…
In this paper, the theory of harmonic maps is extended. The soliton or traveling wave solutions of Euler's equations of the extended harmonic maps are studied. In certain cases, the chaotic behaviors of these partial equations can be found…
We use a composite gravitational galactic model consisting of a disk, a halo, a massive nucleus and a strong nuclear bar, in order to study the connections between global and local parameters in a realistic dynamical system. The local model…