Group automorphisms with few and with many periodic points

2003/06/19 by Thomas Ward
Mathematics · #math.DS #math.NT #msc:37C35 #msc:22D40 #msc:11N13

paper · pdf

published as Proc. Amer. Math. Soc., 133, 91-96, 2005 · amsart latex 6 pages

arxiv created 2003/06/19 · arxiv updated 2009/11/30

Abstract

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