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Group automorphisms with few and with many periodic points

Authors:	Thomas Ward

Institution:	School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom

Abstract:	For each $C\in0,\infty]$ 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.

Keywords:	Group automorphism periodic points topological entropy Lehmer problem

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