Related papers: Quantifying chaos using Lagrangian descriptors
We study the regular or chaotic nature of orbits in a 3D potential describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical calculations show, that the percentage of chaotic orbits decreases exponentially,…
We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by…
A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in…
We adapt the concept of Lagrangian descriptors, which have been recently introduced as efficient indicators of phase space structures in chaotic systems, to unveil the key features of open maps. We apply them to the open tribaker map, a…
Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work…
In this brief, an algorithm for controlling chaotic systems using small, continuous time perturbations is presented. Stabilisation is achieved by self controlling feedback using low order LTI filters. The algorithm alleviates the need of…
We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a flat disk and a central, non spherical and massive nucleus. In particular, we study the…
The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…
We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term…
The onset of stochasticity is measured in $\Lambda$CDM cosmological simulations using a set of classical observables. It is quantified as the local derivative of the logarithm of the dispersion of a given observable (within a set of…
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…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
The local density of states (LDOS) is a distribution that characterizes the effect of perturbations on quantum systems. Recently, it was proposed a semiclassical theory for the LDOS of chaotic billiards and maps. This theory predicts that…
Chaos indicators, like the Lyapunov exponent lambda, are widely used in celestial mechanics to characterize the dynamical behavior of bodies. The stability of their orbit can be determined by the calculation of the local exponential…
Thanks to the simplicity and robustness of its calculation methods, algorithmic (or Kolmogorov) complexity appears as a useful tool to reveal chaotic dynamics when experimental time series are too short and noisy to apply Takens'…
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…
Uncontrolled geostationary satellites abandoned near an unstable equilibrium point of the equator experience irregular transitions between dynamical states (continuous circulation, long and short libration). They are caused by the…