Group automorphisms with few and with many periodic points

Ward, Thomas

doi:10.1090/S0002-9939-04-07626-9

Group automorphisms with few and with many periodic points
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Proc. Amer. Math. Soc. 133 (2005), 91-96 Request permission

Abstract:

For each $C\in [0,\infty ]$ a compact group automorphism $T:X\to X$ is constructed with the property that \[ \frac {1}{n}\log \vert \{x\in X\mid T^n(x)=x\}\vert \longrightarrow C. \] 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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