On the sructure of non-singular iteration groups on the circle.

Ciepliński, Krzysztof

Displaying similar documents to “On the sructure of non-singular iteration groups on the circle.”

The structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

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The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle $𝕊^{1}$ , that is, families $ℱ = {F^{v} 𝕊^{1} ⟶ 𝕊^{1} v \in V}$ of homeomorphisms such that $F^{v_{1}} \circ F^{v_{2}} = F^{v_{1} + v_{2}}, v_{1}, v_{2} \in V,$ 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).