On the Brin Prize work of Artur Avila in Teichmüller dynamics and interval-exchange transformations
type: Item
instance of: scholarly article
title: On the Brin Prize work of Artur Avila in Teichmüller dynamics and interval-exchange transformations
zbMATH Open document ID: 1272.37002
author: Giovanni Forni
published in: Journal of Modern Dynamics
publication date: 2012-10-16T00:00:00Z
review text: This paper reviews the work of Artur Avila and his collaborators (notably G. Forni, S. Gouezel, M. Viana, and J.-C. Yoccoz) on the ergodic properties of interval exchange transformations (IETs) and related problems on the dynamics of the Teichmüller (geodesic) flow. It surveys the connection between IETs and the Teichmüller flow, especially the link between exponents of deviation of ergodic averages for IETS and Lyapunov exponents for the Kontsevich-Zorich cocycle over the Teichmüller flow, and explains (with outlines of proofs) the results of Avila-Viana on simplicity of the Lyapunov spectrum, and Avila-Gouezel-Yoccoz on exponential rates of mixing for the Teichmüller flow. It also discusses his proof (joint with G. Forni) of weak-mixing of almost every interval exchange transformation. It is an eminently readable survey of an impressive sample of Avila's work.
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 37D25
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 37E35
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 6094022
zbMATH Keywords: interval exchange map
zbMATH Keywords: Teichmüller dynamics
zbMATH Keywords: Brin Prize
zbMATH Keywords: Artur Avila
reviewed by: Jayadev S. Athreya
MaRDI profile type: Publication
full work available at URL: jmd.2012.6.139
OpenAlex ID: W2059639219
Wikidata QID: Q56602638
DOI: 10.3934/JMD.2012.6.139
description: scientific article; zbMATH DE number 6094022