Group automorphisms with few and with many periodic points

Abstract

For any $C\in [0,\infty ]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$\frac{1}{n}\log |\{x\in X\mid T^n(x)=x\}|⟶C.$$ This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy.

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