Periodic Points for Expansive Actions of Zd on Compact Abelian Groups

In this note we show that the periodic points of an expansiveZ^d action on a compact abelian group are uniformly distributedwith respect to Haar measure if the action has completely positiveentropy. In the general expansive case, we show that any measureobtained as the distribution of periodic points along some sequenceof periods necessarily has maximal entropy but need not be Haarmeasure.