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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Zero entropy and directional Bernoullicity of a Gaussian $ {\bf Z}\sp 2$-action


Authors: S. Ferenczi and B. Kamiński
Journal: Proc. Amer. Math. Soc. 123 (1995), 3079-3083
MSC: Primary 28D15; Secondary 60G15
MathSciNet review: 1209421
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Abstract: We give an example of a Gaussian $ {\mathbb{Z}^2}$-action $ \Phi $ with zero entropy which is weakly mixing, rigid and such that every non-trivial measure-preserving transformation $ {\Phi ^g}$ defined by $ \Phi , g \in {\mathbb{Z}^2}$, is a Bernoulli shift with infinite entropy.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1209421-9
PII: S 0002-9939(1995)1209421-9
Keywords: Entropy, Gaussian $ {\mathbb{Z}^2}$-actions, spectral measures
Article copyright: © Copyright 1995 American Mathematical Society