Periodic points for expansive actions of Z^d on compact abelian groups

Ward, T

Abstract

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 measure obtained as the distribution of periodic points along some sequence of periods necessarily has maximal entropy but need not be Haar measure.

Citation

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

• Journal Article Type: Article
• Publication Date: Jan 1, 1992
• Deposit Date: Oct 11, 2012
• Publicly Available Date: Oct 16, 2012
• Journal: Bulletin of the London Mathematical Society
• Print ISSN: 0024-6093
• Electronic ISSN: 1469-2120
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 4
• Pages: 317-324
• DOI: https://doi.org/10.1112/blms/24.4.317
• Public URL: https://durham-repository.worktribe.com/output/1502658