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On some iterative roots on the circle

2003
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Publicationes mathematicae (Debrecen)
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The aim of this paper is to investigate the problem of the existence of continuous iterative roots of a homeomorphism F : Let S 1 = {z ∈ C : |z| = 1} be the unit circle with the positive orientation. Let u, w, z ∈ S 1 , then there exist unique t 1 , t 2 ∈ [0, 1) such that we 2πit 1 = z, we 2πit 2 = u. Define −−−→ u, w := e 2πit : t ∈ t u , t w ). This set is said to be an open arc (resp. a closed arc). Let F : S 1 −→ S 1 be a continuous mapping, then there exist a continuous function f : R −→ R

doi:10.5486/pmd.2003.2823
fatcat:qbr6ne67jbfmvpymgxy4jt4rbm