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Zbl 0979.37016
Barton, Reid; Burns, Keith
A simple special case of Sharkovskii's theorem. (English)
[J] Am. Math. Mon. 107, No.10, 932-933 (2000). ISSN 0002-9890

From the text: Let $I\subset \bbfR$ be a bounded closed interval and $f:I\to I$ a continuous map; $f^n$ denotes the $n$-fold composition of $f$ with itself. A point $x\in I$ is a periodic point for $f$ with period $p$ if $f^p(x)= x$ and has least period $p$ if in addition $f^k(x)\ne x$ for $1\leq k\leq p-1$. The note presents a short proof of the following result. \par Proposition. If $f$ has a periodic point is not fixed, then $f$ has a periodic point of least period 2. \par This is a special case of Sharkovskii's famous theorem.

MSC 2000:: *37E05 Maps of the interval

Keywords: periodic point

Cited in: Zbl 0979.37018

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