Strictly ergodic models for non-invertible transformations
type: Item
instance of: scholarly article
title: Strictly ergodic models for non-invertible transformations
zbMATH Open document ID: 0697.28008
DOI: 10.1007/BF02767370
author: N. E. Zubov
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A continuous transformation of a compact metric space Y is said to be strictly ergodic, if there is a unique Borel probability measure \(\nu\), fixed by the action, and \(\nu (U)>0\) for every non-empty open set \(U\subset Y\). In 1969 R. Jewett proved that weakly mixing invertible transformation on a Lebesgue space is measure isomorphic to a strictly ergodic transformation. In 1983 B. Weiss extended this result to any ergodic free action of an elementary amenable group. Using Weiss' method, the author obtains a similar result in the case of non-invertible transformation.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 4142373
zbMATH Keywords: weakly mixing invertible transformation
zbMATH Keywords: strictly ergodic transformation
zbMATH Keywords: non-invertible transformation
reviewed by: V. Ya. Golodets
MaRDI profile type: Publication
cites work: An application of number theory to ergodic theory and the construction of uniquely ergodic models
cites work: Q5183834
cites work: Q5587247
cites work: Strictly ergodic models for dynamical systems
description: scientific article; zbMATH DE number 4142373