Limit theorems for translation flows

Alexander I. Bufetov

doi:https://doi.org/10.4007/annals.2014.179.2.2

Limit theorems for translation flows

Pages 431-499 from Volume 179 (2014), Issue 2 by Alexander I. Bufetov

Abstract

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).

Keywords

Hoelder cocycles, Renormalization, Teichmueller geodesic flow, ergodic integrals, interval exchange transformations, invariant distributions, invariant finitely-additive measures, limit theorems, translation flows

DOI

https://doi.org/10.4007/annals.2014.179.2.2

3152940

zbMATH

06284343

Milestones

Received: 19 March 2010
Revised: 17 August 2012
Accepted: 7 December 2012
Published online: 1 March 2013

Authors

Alexander I. Bufetov

Laboratoire d'Analyse, Topologie, Probabilités, Aix-Marseille Université, CNRS, the Steklov Institute of Mathematics, the Institute for Information Transmission Problems, National Research University Higher School of Economics, the Independent University of Moscow, Rice University