Related papers: Comparative study of variational chaos indicators …
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…
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…
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 present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta,…
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…
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 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…
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular,…
We apply the Smaller ALignment Index (SALI) method to a 4--dimensional mapping of accelerator dynamics in order to distinguish rapidly, reliably and accurately between ordered and chaotic motion. The main advantage of this index is that it…
Full general relativity requires that chaos indicators should be invariant in various spacetime coordinate systems for a given relativistic dynamical problem. On the basis of this point, we calculate the invariant Lyapunov exponents (LEs)…
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 provide a concise presentation of the Smaller (SALI) and the Generalized Alignment Index (GALI) methods of chaos detection. These are efficient chaos indicators based on the evolution of two or more, initially distinct, deviation vectors…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…
We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of…
We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as of the numerical techniques developed for the computation of the maximal, of few and of all of them. After some historical…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
The recurrence-based divergence quantifier ($DIV$), traditionally applied to dissipative systems, is shown here to be an effective finite-time chaos indicator for conservative dynamics. We benchmark its performances against the…
We present and validate simple and efficient methods to estimate the chaoticity of orbits in low dimensional dynamical systems from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for…