A \(C^ 1\)-expanding map on the circle which is not weak-mixing
type: Item
instance of: scholarly article
title: A \(C^ 1\)-expanding map on the circle which is not weak-mixing
zbMATH Open document ID: 0862.28015
DOI: 10.1007/BF02761112
published in: Israel Journal of Mathematics
publication date: 1997-04-16T00:00:00Z
review text: The author constructs an example of a \(C^1\) expanding map of the circle which preserves Lebesgue measure such that the system is ergodic, but not weak-mixing. This contrasts with the case of \(C^{1+ \varepsilon}\) maps, where any such map preserving Lebesgue measure has a Bernoulli natural extension and hence is weak-mixing.
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 878300
zbMATH Keywords: measure-preserving map
zbMATH Keywords: weakly mixing
zbMATH Keywords: \(C^ 1\) expanding map
zbMATH Keywords: weak-mixing
author: Anthony Quas
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
cites work: Generalized baker's transformations
cites work: Mixing examples in the class of piecewise monotone and continuous maps of the unit interval
cites work: Nonuniqueness in \(g\)-functions
cites work: Strongly mixing g-measures
cites work: Q4863617
cites work: Q4880894
cites work: Ruelle's Operator Theorem and g-Measures
description: scientific article; zbMATH DE number 878300