Taylor approximation of invariant fiber bundles for nonautonomous difference equations
type: Item
instance of: scholarly article
title: Taylor approximation of invariant fiber bundles for nonautonomous difference equations
zbMATH Open document ID: 1070.39023
author: Martin Rasmussen
author: Christian Pötzsche
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: The authors develop a method to calculate the Taylor approximation for invariant fiber bundles, which generalize the concept of invariant manifold to nonautonomous difference equations. The motivation for this study is very clear, and the paper is very well written. The applicability of the obtained results to nonautonomous difference equations is illustrated by a good number of examples from mathematical biology, for which the stability properties of the equilibrium is addressed.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 37D10
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 2136807
zbMATH Keywords: invariant manifold
zbMATH Keywords: Taylor approximation
zbMATH Keywords: nonautonomous difference equation
zbMATH Keywords: invariant fiber bundles
zbMATH Keywords: stability
zbMATH Keywords: reduction principle
MaRDI profile type: Publication
full work available at URL: j.na.2004.10.019
OpenAlex ID: W1968620436
cites work: Manifolds, tensor analysis, and applications.
cites work: Q4033029
cites work: The fundamental existence theorem on invariant fiber bundles
cites work: Approximation of attractors of nonautonomous dynamical systems
cites work: Q5700940
cites work: The dichotomy spectrum for noninvertible systems of linear difference equations
cites work: Numerical Taylor expansions of invariant manifolds in large dynamical systems
cites work: Applications of centre manifold theory
cites work: Pullback attractors in dissipative nonautonomous differential equations under discretization
cites work: A subdivision algorithm for the computation of unstable manifolds and global attractors
cites work: Numerical Taylor expansions for invariant manifolds
cites work: Numerical calculation of invariant manifolds for maps
cites work: Multilinear algebra. 2nd ed
cites work: Counting roots of the characteristic equation for linear delay-differential systems
cites work: On the computation of invariant manifolds of fixed points
cites work: Hopf bifurcation from nonperiodic solutions of differential equations. I: Linear theory
cites work: A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles.
cites work: Hopf bifurcation from non-periodic solutions of differential equations. II
cites work: Q3874765
cites work: Pullback attractors in nonautonomous difference equations
cites work: Q4360299
cites work: Global stability in a nonlinear difference-delay equation model of flour beetle population growth
cites work: Oscillations and global attractivity in a discrete delay logistic model
cites work: Elements of applied bifurcation theory
cites work: Q4695311
cites work: Stability, instability, and bifurcation phenomena in non-autonomous differential equations
cites work: Q4846956
cites work: Q4676212
cites work: Q4028588
cites work: Q3744918
DOI: 10.1016/J.NA.2004.10.019
description: scientific article; zbMATH DE number 2136807