A simple special case of Sharkovskii's theorem

Authors: Reid Barton and Keith Burns

Suppose that a continuous map of the interval to itself has a periodic point that is not fixed. Then it must have a periodic point whose least period is exactly two. This result is interesting in its own right and is used in the proof of Sharkovskii's theorem (of which it is a special case). The proof that we give is simple enough to be used in undergraduate courses on dynamical systems.

This article has appeared in the American Mathematical Monthly 107(2000), 932--933. It is available in the following formats:

Authors' addresses:

	Reid Barton
	66 Alpine Street 
 	MA 02474

	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        burns followed by math.northwestern.edu


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