Group automorphisms with few and with many periodic points

Thomas Ward

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Group automorphisms with few and with many periodic points

Thomas Ward

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Abstract

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

Thomas Ward. 2003-06-19. Group automorphisms with few and with many periodic points. https://arxiv.org/abs/math/0306292

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