Hyperbolicity of \(C^1\)-stably expansive homoclinic classes
type: Item
instance of: scholarly article
title: Hyperbolicity of \(C^1\)-stably expansive homoclinic classes
zbMATH Open document ID: 1196.37055
author: Manseob Lee
author: Keonhee Lee
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-06-23T00:00:00Z
review text: The authors consider Diff\((M)\) - the space of diffeomorphisms of the compact \(C^{\infty}\) manifold, endowed with the \(C^1\)-topology. It is shown in the main result of the paper that if there exists some residual subset \(R\subset\text{ Diff}(M)\) such that for any \(f\in R\) and a hyperbolic periodic point \(p\) of \(f\), the homoclinic class \(H_f(p)\) is \(C^{\infty}\)-stable expansive iff it is \(C^{\infty}\)-persistently expansive.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37C05
Mathematics Subject Classification ID: 37C55
zbMATH DE Number: 5725428
zbMATH Keywords: homoclinic class
zbMATH Keywords: \(C^1\)-stably expansive
zbMATH Keywords: hyperbolic
zbMATH Keywords: periodic
MaRDI profile type: Publication
full work available at URL: dcds.2010.27.1133
OpenAlex ID: W2107641585
DOI: 10.3934/DCDS.2010.27.1133
description: scientific article; zbMATH DE number 5725428