A shadowing theorem for ordinary differential equations
type: Item
instance of: scholarly article
title: A shadowing theorem for ordinary differential equations
zbMATH Open document ID: 0826.58027
DOI: 10.1007/BF00952258
author: Brian A. Coomes
author: Hüseyin Koçak
author: Kenneth Palmer
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-05-11T00:00:00Z
review text: A new notion of shadowing of a pseudo orbit, an approximate solution, of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced. Then a general theorem which guarantees the existence of shadowing of pseudo orbits in compact hyperbolic sets is proved.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 34E99
zbMATH DE Number: 753650
zbMATH Keywords: shadowing property
zbMATH Keywords: hyperbolic invariant set
zbMATH Keywords: pseudo orbit
reviewed by: Eugene Ershov
MaRDI profile type: Publication
cites work: Q5566243
cites work: \(\omega\)-limit sets for axiom A diffeomorphisms
cites work: A Shadowing Lemma with Applications to Semilinear Parabolic Equations
cites work: Q3031297
cites work: Q5288482
cites work: Shadowing orbits of ordinary differential equations
cites work: Some lemmas about dynamical systems.
cites work: Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
cites work: Q3831754
cites work: Stability theorems and hyperbolicity in dynamical systems
cites work: Q4340096
cites work: Rigorous verification of trajectories for the computer simulation of dynamical systems
cites work: Q3744918
cites work: GIBBS MEASURES IN ERGODIC THEORY
cites work: Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for \(C^ 1\)-maps in Banach spaces
cites work: Transversal homoclinic points and hyperbolic sets for non-autonomous maps. I
description: scientific article; zbMATH DE number 753650