Group automorphisms with few and with many periodic points

Details Group automorphisms with few and with many periodic points Group automorphisms with few and with many periodic points

2003-06-19

arxiv.org/abs/math/0306292v1

Proc. Amer. Math. Soc., 133, 91-96, 2005

Mathematics

Dynamical Systems

amsart latex 6 pages

Scientific paper

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