Periodic points for expansive actions of Zd on compact Abelian groups

T. B. Ward

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Abstract

In this note we show that the periodic points of an expansive Zd 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 measure obtained as the distribution of periodic points along some sequence of periods necessarily has maximal entropy but need not be Haar measure.
Original languageEnglish
Pages (from-to)317-324
Number of pages8
JournalBulletin of the London Mathematical Society
Volume24
Issue number4
DOIs
Publication statusPublished - 1992

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