Generalizations of the Bonatti-Langevin example of Anosov flow and their classification up to topological equivalence
type: Item
instance of: scholarly article
title: Generalizations of the Bonatti-Langevin example of Anosov flow and their classification up to topological equivalence
zbMATH Open document ID: 0916.58033
author: Thierry Barbot
published in: Communications in Analysis and Geometry
publication date: 1999-07-22T00:00:00Z
review text: The author considers the problem of topological equivalence between Anosov flows. How much do the topological properties of the ambient manifold influence on the dynamical properties of the flow? The author gives a complete classification of Anosov flows on certain 3-manifolds up to topological equivalence. These manifolds are the orientable ones obtained by gluing the nontrivial circle bundle over the two-punctured projective plane along its two boundary components. Moreover, the author presents (apparently) the first known examples of 3-manifolds admitting at the same time \(R\)-covered and non \(R\)-covered Anosov flows.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1267476
zbMATH Keywords: Anosov flow
zbMATH Keywords: 3-manifold
zbMATH Keywords: \(R\)-covered
zbMATH Keywords: non \(R\)-covered Anosov flow
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
DOI: 10.4310/CAG.1998.V6.N4.A5
description: scientific article; zbMATH DE number 1267476