Group automorphisms with few and with many periodic points

For each C ∈ [0,∞] a compact group automorphism T: X → X is constructed with the property that 1 n log|{x ∈ X |T n (x) = x}| → 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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