## A simple special case of Sharkovskii's theorem

**Authors: Reid Barton and Keith Burns **
**Abstract:**

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
Arlington
MA 02474
U.S.A.
Keith Burns
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
U.S.A.
burns followed by math.northwestern.edu

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