Classification of expansive attractors on surfaces
type: Item
instance of: scholarly article
title: Classification of expansive attractors on surfaces
zbMATH Open document ID: 1267.37025
DOI: 10.1017/S0143385710000544
author: Brian F. Martensen
author: Marcy Barge
published in: Ergodic Theory and Dynamical Systems
publication date: 2012-05-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1002.1485
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 37D25
zbMATH DE Number: 6038240
zbMATH Keywords: expansive homeomorphisms
zbMATH Keywords: pseudo-Anosov
zbMATH Keywords: attractors
zbMATH Keywords: transitive
MaRDI profile type: Publication
arXiv ID: 1002.1485
cites work: Expansive attractors on surfaces
cites work: Expansive homeomorphisms of surfaces
cites work: Differentiable dynamical systems
cites work: Rigidity in one-dimensional tiling spaces
cites work: Taming the Cantor fence
cites work: Embedding tiling spaces in surfaces
OpenAlex ID: W2963291647
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review text: In this paper, a topological and dynamical description of expansive attractors on surfaces is obtained. In [Ergodic Theory Dyn. Syst. 26, No. 1, 291--302 (2006; Zbl 1085.37037)], \textit{F. Rodriguez Hertz} and \textit{J. Rodriguez Hertz} conjectured that all transitive expansive attractors are conjugate to either a hyperbolic attractor or a derived from a pseudo-Anosov attractor. Let \(A\) be an attractor for a homeomorphism \(f\) of a compact surface \(M\). Roughly speaking, we say that \(A\) is derived from pseudo-Anosov if there is a pseudo-Anosov surface homeomorphism \(g : S \to S\) which is a factor of \(f : A \to A\). In the paper under review, the above conjecture is proved. To be more precise, it is proved that every non-trivial transitive expansive attractor of a homeomorphism of a compact surface is a derived from pseudo-Anosov attractor.
reviewed by: Kazuhiro Sakai
description: scientific article; zbMATH DE number 6038240