Foliations of surfaces and semi-Markovian subsets of subshifts of finite type
type: Item
instance of: scholarly article
title: Foliations of surfaces and semi-Markovian subsets of subshifts of finite type
zbMATH Open document ID: 0840.58017
DOI: 10.1016/0166-8641(95)00020-H
published in: Topology and its Applications
publication date: 1996-07-09T00:00:00Z
review text: A space \(\mathcal F\) of equivalence classes of measured foliations of a closed surface \(S\) of genus \(g\geq 2\) is defined as the quotient space of Thurston measured foliation space. \({\mathcal M}{\mathcal F}\) by the equivalence relation identifying two elements of \({\mathcal M}{\mathcal F}\) if they can be presented by measured foliations on the surface which agree as foliations, regardless of the transverse measure. It is given the presentation (in the sense of symbolic dynamics) of the action of a pseudo-Anosov mapping class of \(\mathcal M\) in the neighborhood of its attracting fixed point in \(\mathcal F\). It is stated that the action is semi-Markovian.
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 823478
zbMATH Keywords: foliation
zbMATH Keywords: semi-Markovian subset
zbMATH Keywords: subshift of finite type
zbMATH Keywords: mapping class group
author: Athanase Papadopoulos
reviewed by: A. V. Aminova
MaRDI profile type: Publication
cites work: Une Dichotomie de Hopf Pour les Flots Geodesiques Associes Aux Groupes Discrets D'Isometries Des Arbres
cites work: Q4191989
cites work: Q3772406
cites work: Simplicial systems for interval exchange maps and measured foliations
cites work: Interval exchange transformations and measured foliations
cites work: Q3036311
cites work: Combinatorics of Train Tracks. (AM-125)
cites work: A characterization of pseudo-Anosov foliations
cites work: Shorter Notes: Some Simple Examples of Symplectic Manifolds
cites work: On the geometry and dynamics of diffeomorphisms of surfaces
cites work: Gauss measures for transformations on the space of interval exchange maps
Wikidata QID: Q127006571
description: scientific article; zbMATH DE number 823478