# American Institute of Mathematical Sciences

July  2013, 33(7): 2667-2679. doi: 10.3934/dcds.2013.33.2667

## The period set of a map from the Cantor set to itself

 1 Mathematics Department, Brigham Young University, Provo, UT, 84602, United States 2 Mathematics Department, Southern Utah University, Cedar City, UT, 84720, United States 3 Institute of Mathematics, University of Gdańsk ul. Wita Stwosza 57, PL-80952 Gdańsk, Poland

Received  March 2012 Revised  August 2012 Published  January 2013

In this paper we consider all possible period sets $P(f)$ for self-maps of the Cantor set, $f:C\to C$. We prove that the possible period sets are completely unrestricted provided that, in addition, one allows points that are not periodic. However, if every point is periodic, we show that a surprising finiteness condition is imposed on $P(f)$: namely, there is a finite subset $B$ of $P(f)$ such that every element of $P(f)$ is divisible by at least one element of $B$.
Citation: James W. Cannon, Mark H. Meilstrup, Andreas Zastrow. The period set of a map from the Cantor set to itself. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2667-2679. doi: 10.3934/dcds.2013.33.2667
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