Stretching rates in discrete dynamical systems
type: Item
instance of: scholarly article
title: Stretching rates in discrete dynamical systems
zbMATH Open document ID: 0963.37080
DOI: 10.1016/S0960-0779(98)00208-2
author: R. Tiebel
published in: Chaos, Solitons and Fractals
publication date: 2000-08-09T00:00:00Z
review text: The asymptotic behaviour of trajectories in nonlinear dynamical systems in \(\mathbb{R}^n\) (for \(t\to\infty)\) can be characterized by stretching and/or shrinking rates of volume elements in different directions. Fixed points, cycles, tori and chaotic attractors are different types of attractors, which are distinguishable by their Lyapunov exponents connected with these stretching rates. The author shows that the singular value decomposition of the Jacobian matrix is a useful technique for calculating the maximal stretching rates and the corresponding maximal Lyapunov exponents.
Mathematics Subject Classification ID: 37M25
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1486540
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: attractor
zbMATH Keywords: stretching rate
zbMATH Keywords: singular value decomposition
reviewed by: Messoud Efendiev
describes a project that uses: Dynamics
MaRDI profile type: Publication
cites work: Q4309546
cites work: Q4183797
cites work: Q3135098
cites work: Dynamics: numerical explorations. Accompanying computer program dynamics. Coauthored by Eric J. Kostelich. With 3 1/2'' DOS Diskette
description: scientific article; zbMATH DE number 1486540