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Characterizing orbit structures of homeomorphisms on Cantor sets

Volume 245 / 2019

Casey Sherman Fundamenta Mathematicae 245 (2019), 1-24 MSC: Primary 54H20. DOI: 10.4064/fm652-10-2018 Published online: 2 January 2019


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.


  • Casey ShermanDepartment of Mathematics
    St. Edward’s University
    3001 S. Congress Ave.
    Austin, TX 78704, U.S.A.

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