The relative Lyapunov indicator: an efficient method of chaos detection
type: Item
instance of: scholarly article
title: The relative Lyapunov indicator: an efficient method of chaos detection
zbMATH Open document ID: 1109.37033
author: Zsolt Sándor
author: Érdi Bálint
author: András Széll
author: B. Funk
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-03-01T00:00:00Z
review text: In recent years there has been a growing interest in the development and application of different chaos detection methods. Besides the traditional tools, i.e. maximum Lyapunov characteristic exponent, frequency analysis etc. several new methods have been developed, which can be used to detect ordered and chaotic nature of individual orbits, or to separate regions of ordered and chaotic motions in the phase space of a dynamical system. One of these methods is the fast Lyapunov indicator (FLI) method. The time evolution of the FLI indicates clearly the ordered or chaotic nature of an orbit. Here, a new chaos detection method called the relative Lyapunov indicator (RLI) is introduced. The definition of the RLI is complex enough and connected with the Lyapunov characteristic exponent (LCE) and its finite-time approximation called the finite-time Lyapunov indicator (LI). An application of the RLI method to symplectic mappings and to a continuous Hamiltonian system (the restricted four-body problem related with the exo-planetary system) is considered.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 37N05
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70K55
zbMATH DE Number: 2140272
zbMATH Keywords: celestial mechanics
zbMATH Keywords: dynamical systems
zbMATH Keywords: chaos and regular regions
zbMATH Keywords: Lyapunov indicators
MaRDI profile type: Publication
full work available at URL: s10569-004-8129-4
OpenAlex ID: W1971410414
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DOI: 10.1007/S10569-004-8129-4
description: scientific article; zbMATH DE number 2140272