Related papers: Chaos in core-halo gravitating systems
We study the dynamical instability in spherical gravitating systems with core using the Ricci curvature criterion. By means of numerical estimations of the Ricci curvature for static N-body systems, it is shown that the core can both,…
A geometric method, using the Ricci (or mean) curvature of the Lagrangian (configuration) manifold, is used to study the relative instability of evolving $N$-body gravitating systems with massive centres. The performed numerical experiments…
I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries (a double star, a double black hole, a binary asteroid, etc.) is estimated analytically, in function of the…
We stress that halo dipole components are nontrivial in core-halo systems in both Newton's gravity and General Relativity. To this end, we extend a recent exact relativistic model to include also a halo dipole component. Next, we consider…
In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…
Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
The motion of stars in the gravitational potential of a triaxial galaxy is generically chaotic. However, the timescale over which the chaos manifests itself in the orbital motion is a strong function of the degree of central concentration…
We clarify some points about the systems considered by Sota, Suzuki and Maeda in Class. Quantum Grav. 13, 1241 (1996). Contrary to the authors' claim for a non-homoclinic kind of chaos, we show the chaotic cases they considered are…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
It is shown how the violation of the invariance of the $Z$-component of the orbital angular momentum $L_z$ in the axially symmetric potential of the Galaxy with a bar can serve as an indicator of the degree of orbital chaos of globular…
This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes…
We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…
Manifestation of dynamical instability and Hamiltonian chaos in the fundamental near-resonant matter-radiation interaction has been found analitically and in a Monte Carlo simulation in the behavior of atoms moving in a rigid optical…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The Ricci curvature criterion is used for the investigation of the relative instability of several configurations of N-body gravitating systems. It is shown, that the systems with double massive centers are more unstable than the…
We use a simple dynamical model in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central, spherically symmetric, dense nucleus and a flat disk. In particular, we explore how the total orbital…
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…