On the Hartman-Grobman theorem for maps
type: Item
instance of: scholarly article
title: On the Hartman-Grobman theorem for maps
zbMATH Open document ID: 0597.58022
DOI: 10.1016/0022-0396(86)90085-9
author: Juergen Quandt
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The Hartman-Grobman theorem says that in a neighborhood of a hyperbolic fixed point a diffeomorphism is topologically conjugate to its derivative at that fixed point. A generalization of this theorem to a hyperbolic automorphism L of a Banach space X is also known. The author extends this to the case of a hyperbolic endomorphism L of X. Namely, he proves that the maps \(\phi_ j=L+f_ j\), \(j=1,2\) where \(f_ j: X\to X\) are Lipschitz with \(lip(f_ j)\) small enough, are inverse limit conjugate by a homeomorphism which maps orbits of \(\phi_ 1\) to orbits of \(\phi_ 2\). An application to evolution equations is given.
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 3962806
zbMATH Keywords: Hartman-Grobman theorem
zbMATH Keywords: hyperbolic fixed point
zbMATH Keywords: evolution equations
reviewed by: Yuri Kifer
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90085-9
OpenAlex ID: W1981879521
cites work: An introduction to infinite dimensional dynamical systems -- geometric theory. With an appendix by Krzysztof P. Rybakowski
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cites work: Q5575928
cites work: On a Theorem of P. Hartman
cites work: On inverse limit stability for maps
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description: scientific article; zbMATH DE number 3962806