On conjugacy of disjoint iteration groups on the unit circle - Ciepliński, Krzysztof (Annales Mathematicae Silesianae, 1999)
The aim of this paper is to give a necessary and sufficient condition for conjugacy of some iteration groups ???? = Ft : S↦S, t∈ℝ and ???? = Gt : S↦S, t∈ℝ defined on the unit circle S. Our basic assumption is that the yare non-singular, that is at least one element of ???? and ???? has no periodic point. Moreover, under some further restrictions, we determine all orientation-preserving homeomorphisms Γ : S↦S such that Γ◦Ft = Gt◦Γ, t∈ℝ.