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On some properties of orientation-preserving surjections on the circle. (English) Zbl 1164.37013
The author generalizes the known fact that every two periodic points of an orientation-preserving homeomorphism of the circle have the same period (cf. Theorem 1) proving what follows. If \(B \subset S^1\), \({\operatorname {card}}\, B\geq 3\) and \(F\colon B\rightarrow B\) is an orientation-preserving surjection with \({\operatorname {Per}}\, F \not = \emptyset \), then every two periodic points of \(F\) have the same period. He also presents some properties of orientation-preserving surjections with a finite and non-empty set of periodic points.

MSC:
37E10 Dynamical systems involving maps of the circle
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