# zbMATH — the first resource for mathematics

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