Diffeomorphisms with \(C^1\)-stably average shadowing
type: Item
instance of: scholarly article
title: Diffeomorphisms with \(C^1\)-stably average shadowing
zbMATH Open document ID: 1261.37015
author: Manseob Lee
author: Xiao Wen
publication date: 2013-03-19T00:00:00Z
review text: The authors consider the notion of ``\(C^1\)-stably average shadowing property'' for \(C^1\)-diffeomorphisms \(f\) on a closed \(C^\infty\) manifold \(M\). The main result states that if \(f\) has the \(C^1\)-stably average shadowing property on a transitive set \({\Lambda\subset M}\), which is not a periodic orbit, then \(\Lambda\) admits a dominated splitting. The proof is based on the perturbation along the periodic orbits and the approximation for \(\Lambda\) by periodic orbits of some diffeomorphisms \(g_n\) converging to \(f\) in the \(C^1\) topology .
Mathematics Subject Classification ID: 37D30
Mathematics Subject Classification ID: 37C50
zbMATH DE Number: 6146289
zbMATH Keywords: average shadowing
zbMATH Keywords: dominated splitting
zbMATH Keywords: transitive set
zbMATH Keywords: average pseudo-orbit
reviewed by: Ivan Podvigin
MaRDI profile type: Publication
full work available at URL: s10114-012-1162-4
OpenAlex ID: W2080685115
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DOI: 10.1007/S10114-012-1162-4
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6146289