The ergodic theorem for topological cocycles
type: Item
instance of: scholarly article
title: The ergodic theorem for topological cocycles
zbMATH Open document ID: 0956.37001
author: Nelson G. Markley
author: Kathleen Madden
published in: Rocky Mountain Journal of Mathematics
publication date: 2001-03-12T00:00:00Z
full work available at URL: CONT29-1.html
review text: In Ergodic Theory Dyn. Syst. 11, 19-39 (1991; Zbl 0723.60008), \textit{D. Boivin} and \textit{Y. Derriennic} published a definitive cocycle ergodic theorem generalizing the Birkhoff individual ergodic theorem in the context of a measurable action of the integer lattice \(\mathbb{Z}^m\) or the vector space \(\mathbb{R}^m\). The purpose of this paper is to show that for continuous cocycles an ergodic theorem of the same type can be proved by a more elementary approach using the original Birkhoff individual ergodic theorem and the Poincaré recurrence theorem with an application of the Ascoli lemma.
Mathematics Subject Classification ID: 37A20
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 37A30
zbMATH DE Number: 1309618
zbMATH Keywords: cocycle
zbMATH Keywords: ergodic theorem
reviewed by: Michael L. Blank
MaRDI profile type: Publication
OpenAlex ID: W2014763263
DOI: 10.1216/RMJM/1181071688
description: scientific article; zbMATH DE number 1309618