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The structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle 𝕊 1 , that is, families = { F v 𝕊 1 𝕊 1 v V } of homeomorphisms such that F v 1 F v 2 = F v 1 + v 2 , v 1 , v 2 V , and each F v either is the identity mapping or has no fixed point ( ( V , + ) is an arbitrary 2 -divisible nontrivial (i.e., c a r d V > 1 ) abelian group).

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