The bernoulli property for expansive ℤ2 actions on compact groups

Ward, T. B. (1992) The bernoulli property for expansive ℤ2 actions on compact groups. Israel Journal of Mathematics, 79 (2-3). pp. 225-249. ISSN 0021-2172

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Abstract

We show that an expansive Z2 action on a compact abelian group is measurably isomorphic to a two-dimensional Bernoulli shift if and only if it has completely positive entropy. The proof uses the algebraic structure of such actions described by Kitchens and Schmidt and an algebraic characterisation of the K property due to Lind, Schmidt and the author. As a corollary, we note that an expansive Z2-action on a compact abelian group is measurably isomorphic to a Bernoulli shift relative to the Pinsker algebra. A further corollary applies an argument of Lind to show that an expansive K action of Z2 on a compact abelian group is exponentially recurrent. Finally an example is given of measurable isomorphism without topological conjugacy for Z2-actions.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	15 Dec 2022 02:10
URI:	https://ueaeprints.uea.ac.uk/id/eprint/18594
DOI:	10.1007/BF02808217

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