Stably ergodic diffeomorphisms
type: Item
instance of: scholarly article
title: Stably ergodic diffeomorphisms
zbMATH Open document ID: 0824.58032
DOI: 10.2307/2118602
author: Michael Shub
author: Matthew A. Grayson
author: Charles Pugh
published in: Annals of Mathematics. Second Series
publication date: 1995-04-09T00:00:00Z
review text: This paper considers the existence of open sets \(U\) in an appropriate space of smooth functions on a compact manifold, with the property that each \(f\in U\) is ergodic. Maps in \(U\) are called stably ergodic. Anosov diffeomorphisms have this property, in addition to the stronger properties of uniform hyperbolicity and structural stability. This paper gives examples of stably ergodic diffeomorphisms that are neither hyperbolic nor structurally stable. The main result is that if \(M\) is the unit tangent bundle of a surface of constant negative curvature and if \(f\) is the time-one map of the geodesic flow on \(M\), then \(f\) is stably ergodic with respect to volume preserving transformations that are \(C^ 2\) small.
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 28D10
zbMATH DE Number: 742784
zbMATH Keywords: stably ergodic diffeomorphisms
reviewed by: Mike Hurley
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118602
OpenAlex ID: W82963651
description: scientific article; zbMATH DE number 742784