Characterizing orbit structures of homeomorphisms on Cantor sets
Volume 245 / 2019
Fundamenta Mathematicae 245 (2019), 1-24
MSC: Primary 54H20.
DOI: 10.4064/fm652-10-2018
Published online: 2 January 2019
Abstract
We consider the following problem: If $X$ is a Cantor set and $T:X\to X$ is a homeomorphism, what possible orbit structures can $T$ have? The question is answered in terms of the orbit spectrum of $T$. We also show that the question cannot be answered in terms of the orbit spectrum alone if $T$ is assumed only to be continuous.
