Dynamics of numerical approximations
type: Item
instance of: scholarly article
title: Dynamics of numerical approximations
zbMATH Open document ID: 0911.65063
DOI: 10.1016/S0096-3003(97)81644-X
author: Jack K. Hale
published in: Applied Mathematics and Computation
publication date: 1999-04-22T00:00:00Z
review text: The perturbation of hyperbolic invariant sets of dynamical systems are studied when the system is approximated numerically. A result by \textit{B. Fiedler} and \textit{J. Scheurle} [Discretization of homoclinic orbits \dots, Mem. Am. Math. Soc. 570, 79p. (1996)] is used stating that the numerically approximated flow is the exact flow of some perturbed system. This is used to obtain results on the behavior of equilibrium points, periodic orbits, and tori under discretization in time. Results on the preservation of structural stability for gradient systems are presented. The last section gives open problems.
reviewed by: Karin Gatermann
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 1183183
zbMATH Keywords: invariant set
zbMATH Keywords: numerical approximation
zbMATH Keywords: periodic orbits
zbMATH Keywords: invariant tori
zbMATH Keywords: structural stability
zbMATH Keywords: gradient systems
zbMATH Keywords: dynamical systems
zbMATH Keywords: flow
MaRDI profile type: Publication
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full work available at URL: s0096-3003(97)81644-x
OpenAlex ID: W2004749554
description: scientific article; zbMATH DE number 1183183