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The Bernoulli property for expansive Z^2 actions on compact groups (1992)
Journal Article
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

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 Kitch... Read More about The Bernoulli property for expansive Z^2 actions on compact groups.

Periodic points for expansive actions of Z^d on compact abelian groups (1992)
Journal Article
Ward, T. (1992). Periodic points for expansive actions of Z^d on compact abelian groups. Bulletin of the London Mathematical Society, 24(4), 317-324. https://doi.org/10.1112/blms/24.4.317

In this note we show that the periodic points of an expansive Z^d action on a compact abelian group are uniformly distributed with respect to Haar measure if the action has completely positive entropy. In the general expansive case, we show that any... Read More about Periodic points for expansive actions of Z^d on compact abelian groups.