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1998/1999 A Note on Periodic Points and Commuting Functions
T. H. Steele
Real Anal. Exchange 24(2): 781-790 (1998/1999).


Alikhani-Koopaei has recently conjectured that two commuting continuous functions typically share no periodic points. After discussing the history behind Alikhani-Koopaei's conjecture, we use the Baire Category Theorem to investigate the likelihood that two commuting continuous functions have disjoint sets of periodic points, as well as the structure of the set $\mathcal{F}=\{g\in C(I,I):gf=fg\}$. We then turn our attention to the iterative properties possessed by commuting pairs of continuous functions.


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T. H. Steele. "A Note on Periodic Points and Commuting Functions." Real Anal. Exchange 24 (2) 781 - 790, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0962.54030
MathSciNet: MR1704749

Primary: 54C50

Keywords: $\omega$-limit set , commuting functions , periodic point

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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