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A theorem of Šarkovskii characterizing continuous maps of zero topological entropy. (English) Zbl 0686.26002
Let f be a continuous map of the compact real interval I into itself, $$f_ n$$ the n-th iterate of f. For any $$x\in I$$ $$\omega_ f(x)$$ is the limit set of the sequence $$\{f^ n(x)\}^{\infty}_{n=1}.$$
The main aim of the paper is to give a new and short proof of the following result by A. N. Šarkovskii: f has a periodic point of period different from $$2^ n$$ for any n if and only if there exists $$x\in I$$ such that $$\omega_ f(x)$$ is infinite and contains a periodic point.
Reviewer: K.Janková
##### MSC:
 26A18 Iteration of real functions in one variable 54H25 Fixed-point and coincidence theorems (topological aspects)
##### References:
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