Mather measures and the Bowen-Series transformation.
type: Item
instance of: scholarly article
title: Mather measures and the Bowen-Series transformation.
zbMATH Open document ID: 1114.37018
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2006-11-15T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78706
review text: The paper studies a particular compact Riemann surface \(M\) of genus 2 and constant negative curvature. A ``geodesic billiard'' is defined in terms of the geodesic flow on the unit tangent bundle. An explicit description of \(M\) as a quotient space of a specific octagonal domain in the hyperbolic disk is used to define a Bowen-Series transformation \(T\) of the circle at infinity, and a natural extension \(\hat{T}\) of \(T\) is described, such that there is an isomorphism between the geodesic billiard and a certain suspension of \(\hat{T}\). The correspondence under this isomorphism of invariant measures, Mather minimal measures, and of homological/cohomological data is described in detail.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37E40
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 5072656
zbMATH Keywords: stable norm
zbMATH Keywords: Mather measures
zbMATH Keywords: minimizing measures
zbMATH Keywords: Bowen-series transformations
zbMATH Keywords: geodesic billiard
author: A. O. Lopes
author: Ph. Thieullen
reviewed by: Mike Hurley
MaRDI profile type: Publication
OpenAlex ID: W2005680417
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DOI: 10.1016/J.ANIHPC.2004.12.005
description: scientific article; zbMATH DE number 5072656