\(C^1\)-stably weakly shadowing homoclinic classes admit dominated splittings
type: Item
instance of: scholarly article
title: \(C^1\)-stably weakly shadowing homoclinic classes admit dominated splittings
zbMATH Open document ID: 1195.37011
author: Shaobo Gan
author: Kazuhiro Sakai
author: Lan Wen
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-05-06T00:00:00Z
review text: The aim of the present paper is to introduce the notino of J\(C^1\)-stably weakly shadowing for a closed \(f\)-invariant set where \(f\) is a diffeomorphism defined in a closed \(n\)-dimensional \(C^\infty\) manifold. If \(p\) is a hyperbolic saddle periodic point of \(f\) is proved that the homoclinic class \(H_f(p)\) of \(p\), if \(f|_{H_f(p)}\) is \(C^1\)-stably the splitting on \(H_f(p)\) is partially hyperbolic and if in additon, \(f\) is far from homoclinic tagency, then \(H_f(p)\) is strongly partially hyperbolic.
reviewed by: Juan L. G. Guirao
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37C50
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37D30
zbMATH DE Number: 5704398
zbMATH Keywords: weak shadowing
zbMATH Keywords: pseudo-orbit
zbMATH Keywords: shadowing
zbMATH Keywords: chain recurrent set
zbMATH Keywords: chain component
zbMATH Keywords: homoclinic class
zbMATH Keywords: dominated splitting
zbMATH Keywords: partially hyperbolic
MaRDI profile type: Publication
full work available at URL: dcds.2010.27.205
OpenAlex ID: W2093194459
DOI: 10.3934/DCDS.2010.27.205
description: scientific article; zbMATH DE number 5704398