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Iterative roots of homeomorphisms possessing periodic points. (English) Zbl 1148.39021
This paper is a continuation of the study of many mathematicians devoted to the existence of iterative roots of a given orientation-preserving homeomorphism \(F: S^1 \to S^1\), where \(S^1\) is the unit circle, i.e., the study of the set \(\{ z \in S^1: \exists k \in \mathbf{N}, F^{(k)}(z) = z \}\). The results are based on the deep investigations of the Schröder functional equation \(\psi[F(z)] = e^{2 \pi \alpha} \psi(z)\).

MSC:
39B12 Iteration theory, iterative and composite equations
26A18 Iteration of real functions in one variable
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