Related papers: A new dynamical indicator for chaos detection in g…
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…
In the present article, we present a new gravitational galactic model, describing motion in elliptical as well as in disk galaxies, by suitably choosing the dynamical parameters. Moreover, a new dynamical parameter, the S(g) spectrum, is…
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 efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new…
We study the regular or chaotic character of orbits in a 3D dynamical model, describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical experiments suggest that the percentage of chaotic orbits decreases…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
In the present article, we introduce and also deploy a new, simple, very fast and efficient method, the Fast Norm Vector Indicator (FNVI) in order to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian…
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…
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…
A 3D dynamical model is used to study the motion in the central parts of an elliptical galaxy, hosting a massive and dense nucleus. Our aim is to investigate the regular or chaotic character of the motion, with emphasis in the different…
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 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,…
From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of…
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…
In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret,…
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
The Smaller Alignment Index (SALI) is a very useful and efficient indicator that can distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This is based on the different behavior of the SALI in…
We investigate the properties of motion in a map model derived from a galactic Hamiltonian made up of perturbed elliptic oscillators. The phase space portrait is obtained in all three different cases using the map and numerical integration…
Automatic differentiation provides an efficient means of computing derivatives of complex functions with machine precision, thereby enabling differentiable simulation. In this work, we propose the use of the norm of the tangent map,…