On conjugacy of disjoint iteration groups on the unit circle

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On conjugacy of disjoint iteration groups on the unit circle

Krzysztof Ciepliński-1999-01-01-UNIVERSITY OF SILESIA PRESS (University of Silesia)

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TL;DRAbstract

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 thatΓ◦Ft = Gt◦Γ, t∈ℝ.

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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 thatΓ◦Ft = Gt◦Γ, t∈ℝ.

Keywords

Conjugacy classDisjoint setsUnit circleMathematicsUnit (ring theory)CombinatoricsMathematics education

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