A simple special case of Sharkovskii's theorem

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:

• Tex file
• dvi file
• Postscript file
• pdf file

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