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The Bernoulli property for expansive Z^2 actions on compact groups

Ward, T

The Bernoulli property for expansive Z^2 actions on compact groups Thumbnail


Authors

T Ward



Abstract

We show that an expansive Z^2 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 Z^2-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 Z^2 on a compact abelian group is exponentially recurrent. Finally an example is given of measurable isomorphism without topological conjugacy for Z^2-actions.

Citation

Ward, T. (1992). The Bernoulli property for expansive Z^2 actions on compact groups. Israel Journal of Mathematics, 79(2-3), 225-249. https://doi.org/10.1007/bf02808217

Journal Article Type Article
Publication Date Jan 1, 1992
Deposit Date Oct 11, 2012
Publicly Available Date Oct 16, 2012
Journal Israel Journal of Mathematics
Print ISSN 0021-2172
Electronic ISSN 1565-8511
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 79
Issue 2-3
Pages 225-249
DOI https://doi.org/10.1007/bf02808217

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The original publication is available at www.springerlink.com





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