Hyperbolic trajectories of time discretizations
type: Item
instance of: scholarly article
title: Hyperbolic trajectories of time discretizations
zbMATH Open document ID: 1066.65155
author: Aaron Hagen
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-22T00:00:00Z
review text: The authors investigate the hyperbolic trajectories of time discretizations. They address the problem of persistence of the trajectories of time discretizations. Conditions which guarantee the existence of a mirror trajectory for the underling vector field are given. Estimates are provided for the important quantities in terms of the problem parameters. In addition the Lyapunov-Perron method is implemented as a numerical algorithm for stable/unstable manifolds of fixed points. The authors also provide the foundation for a rigorous implementation of the Lyapunov-Perron method for computing the trajectories, for example periodic orbits.
Mathematics Subject Classification ID: 65P40
Mathematics Subject Classification ID: 37C50
Mathematics Subject Classification ID: 37M05
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 37D05
zbMATH DE Number: 2117565
zbMATH Keywords: hyperbolicity
zbMATH Keywords: shadowing
zbMATH Keywords: time discretization
zbMATH Keywords: periodic orbits
zbMATH Keywords: fixed points
zbMATH Keywords: Lyapunov-Perron method
zbMATH Keywords: stable/unstable manifolds
zbMATH Keywords: numerical dynamics
zbMATH Keywords: long time approximation
zbMATH Keywords: exponential dichotomy
zbMATH Keywords: hyperbolic trajectories
zbMATH Keywords: persistence
reviewed by: Seenith Sivasundaram
MaRDI profile type: Publication
full work available at URL: j.na.2004.07.005
OpenAlex ID: W2060723569
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DOI: 10.1016/J.NA.2004.07.005
description: scientific article; zbMATH DE number 2117565