Abundance of stable ergodicity
type: Item
instance of: scholarly article
title: Abundance of stable ergodicity
zbMATH Open document ID: 1052.37023
author: C. Bonatti
author: Carlos Matheus
author: Marcelo Viana
author: Amie Wilkinson
published in: Commentarii Mathematici Helvetici
publication date: 2004-11-05T00:00:00Z
review text: Summary: We consider the set \({\mathcal P}{\mathcal H}_\omega(M)\) of volume-preserving partially hyperbolic diffeomorphisms on a compact manifold having one-dimensional center bundle. We show that the volume measure is ergodic, and even Bernoulli, for any \(C^2\) diffeomorphism in an open and dense subset of \({\mathcal P}{\mathcal H}_\omega(M)\). This solves a conjecture of \textit{C. Pugh} and \textit{M. Shub} [J. Complexity 13, 125--179 (1997; Zbl 0883.58029)], in this setting.
Mathematics Subject Classification ID: 37D30
Mathematics Subject Classification ID: 37D25
Mathematics Subject Classification ID: 37A25
zbMATH DE Number: 2113819
zbMATH Keywords: partial hyperbolicity
zbMATH Keywords: stable ergodicity
zbMATH Keywords: accessibility
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: nonuniform hyperbolicity
MaRDI profile type: Publication
full work available at URL: s00014-004-0819-8
OpenAlex ID: W2143041686
DOI: 10.1007/S00014-004-0819-8
description: scientific article; zbMATH DE number 2113819