Related papers: A new dynamical indicator for chaos detection in g…
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…
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…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
To investigate non-linear dynamical systems, like for instance artificial satellites, Solar System, exoplanets or galactic models, it is necessary to have at hand several tools, such as a reliable dynamical indicator. The aim of the present…
This paper summarises a numerical investigation which aimed to identify and characterise regular and chaotic behaviour in time-dependent Hamiltonians H(r,p,t) = p^2/2 + U(r,t), with U=R(t)V(r) or U=V[R(t)r], where V(r) is a polynomial in x,…
The orbits of two individual planets in two known binary star systems, \gamma Cephei and HD 196885 are numerically integrated using various numerical techniques to assess the chaotic or quasi-periodic nature of the dynamical system…
We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
An important point in analysing the dynamics of a given stellar or planetary system is the reliable identification of the chaotic or regular behaviour of its orbits. We introduce here the program LP-VIcode, a fully operational code which…
To determine the regular or chaotic nature of the orbits in dynamical systems can be quite an issue. In this article, following Vozikis et al. (2000), we propose a new tool, namely, the Power Spectrum Indicator (PSI), $\psi^2$, that enables…
The behavior of the Generalized Alignment Index (GALI) method has been extensively studied and successfully applied for the detection of chaotic motion in conservative Hamiltonian systems, yet its application to non-Hamiltonian dissipative…
We present here a new method which applies well ordered symbolic dynamics to find unstable periodic and non-periodic orbits in a chaotic system. The method is simple and efficient and has been successfully applied to a number of different…
The Lyapunov Characteristic Exponents are a useful indicator of chaos in astronomical dynamical systems. They are usually computed through a standard, very efficient and neat algorithm published in 1980. However, for Hamiltonian systems the…
We introduce a new methodology for a fast and reliable discrimination between ordered and chaotic orbits in multidimensional Hamiltonian systems which we call the Linear Dependence Index (LDI). The new method is based on the recently…
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…
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…
We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos…
The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of…