Partial hyperbolicity and robust transitivity
type: Item
instance of: scholarly article
title: Partial hyperbolicity and robust transitivity
zbMATH Open document ID: 0987.37020
DOI: 10.1007/BF02392945
author: R. Ures
author: L. J. Díaz
author: Enrique R. Pujals
published in: Acta Mathematica
publication date: 2000-12-06T00:00:00Z
review text: Let \(M\) denote a three-dimensional boundaryless compact manifold and \(\text{Diff}(M)\) the space of \(C^1\)-diffeomorphism defined on \(M\) endowed with the usual \(C^1\)-topology. The maximal invariant set of \(\varphi\) in an open set \(U\), denoted by \(\Lambda_\varphi(U)\), is the set of points whose whole orbit is contained in \(U\). This paper is devoted to the hyperbolicity (uniform partial and strong partial) of \(\Lambda_4(U)\) derived from its robust transitivity. In the case \(U=M\), \(\varphi\) is robustly transitive.
Mathematics Subject Classification ID: 37D30
Mathematics Subject Classification ID: 37C20
zbMATH DE Number: 1541213
zbMATH Keywords: compact manifold
zbMATH Keywords: robust transitivity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02392945
OpenAlex ID: W2046851121
description: scientific article; zbMATH DE number 1541213