On conjugacy of disjoint iteration groups on the unit circle

Krzysztof Ciepliński

Published: 1999-09-30

Vol. 13 (1999)

On conjugacy of disjoint iteration groups on the unit circle

Krzysztof Ciepliński

Abstract

The aim of this paper is to give a necessary and sufficient condition for conjugacy of some iteration groups ???? = {F^t : S↦S, t∈ℝ} and ???? = {G^t : 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◦F^t = G^t◦Γ, t∈ℝ.

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Ciepliński, K. (1999). On conjugacy of disjoint iteration groups on the unit circle. Annales Mathematicae Silesianae, 13, 103–118. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14141

Vol. 13 (1999)
Published: 1999-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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