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Group automorphisms with few and with many periodic points

Author(s): Thomas Ward
Journal: Proc. Amer. Math. Soc. 133 (2005), 91-96.
MSC (2000): Primary 37C35, 22D40, 11N13
Posted: August 10, 2004
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Abstract: For each $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that

\begin{displaymath}\frac{1}{n}\log\vert\{x\in X\mid T^n(x)=x\}\vert\longrightarrow C. \end{displaymath}

This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms with any given topological entropy exist.

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Additional Information:

Thomas Ward
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: t.ward@uea.ac.uk

DOI: 10.1090/S0002-9939-04-07626-9
PII: S 0002-9939(04)07626-9
Keywords: Group automorphism, periodic points, topological entropy, Lehmer problem
Received by editor(s): August 16, 2003
Posted: August 10, 2004
Communicated by: Michael Handel
Copyright of article: Copyright 2004, American Mathematical Society

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The following works have cited this article

Everest, G.; Miles, R.; Stevens, S.; Ward, T., Orbit-counting in non-hyperbolic dynamical systems, J. Reine Angew. Math. 608 (2007), 155-182. MR 2339472

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