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

Ward, T

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Authors

T Ward



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

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Copyright Statement
This is a pre-copy-editing author-produced PDF of an article accepted for publication in Bulletin of the London Mathematical Society following peer review. The definitive publisher-authenticated version Ward, T. (1992) 'Periodic points for expansive actions of Z^d on compact abelian groups.', Bulletin of the London Mathematical Society., 24 (4). pp. 317-324 is available online at: http://dx.doi.org/10.1112/blms/24.4.317





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