Group automorphisms with few and with many periodic points

الأصل · EN

For any C∈[0,∞] a compact group automorphism T:X→ X is constructed with the property that 1/n|{x∈ X Tⁿ(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.