Zero entropy and directional Bernoullicity of a Gaussian 𝑍²-action

Ferenczi, S.; Kamiński, B.

doi:10.1090/S0002-9939-1995-1209421-9

Zero entropy and directional Bernoullicity of a Gaussian $\textbf {Z}^ 2$-action
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by S. Ferenczi and B. Kamiński PDF

Proc. Amer. Math. Soc. 123 (1995), 3079-3083 Request permission

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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