On conjugacy of disjoint iteration groups on the unit circle
Abstract
The aim of this paper is to give a necessary and sufficient condition for conjugacy of some iteration groups 𝓕 = {Ft : S↦S, t∈ℝ} and 𝓖 = {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 𝓕 and 𝓖 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.
References
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Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
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