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arXiv · 1905.09966

New Examples of Bernoulli Algebraic Actions

Douglas Lind·Klaus Schmidt
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Abstract

We give examples of principal algebraic actions of the noncommutative free group $F$ of rank two, as well as other groups, by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism to a Bernoulli action of the group. The isomorphism is defined using homoclinic points, a method that has been used earlier to construct symbolic covers of algebraic actions. To our knowledge, these are the first nontrivial examples of the Bernoullicity of an algebraic action of $F$.

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Douglas Lind, Klaus Schmidt. 2019-05-23. New Examples of Bernoulli Algebraic Actions. https://doi.org/10.1017/etds.2021.56

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