Rotated odometers and actions on rooted trees
| Autor: | Bruin, H., Lukina, O. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Fundamenta Mathematicae, 260, 233-249. Institute of Mathematics, Polish Academy of Sciences |
| ISSN: | 1730-6329 0016-2736 |
| Popis: | A rotated odometer is an infinite interval exchange transformation (IET) obtained as a composition of the von Neumann-Kakutani map and a finite IET of intervals of equal length. In this paper, we consider rotated odometers for which the finite IET is of intervals of length $2^{-N}$, for some $N \geq 1$. We show that every such system is measurably isomorphic to a $\mathbb{Z}$-action on a rooted tree, and that the unique minimal aperiodic subsystem of this action is always measurably isomorphic to the action of the adding machine. We discuss the applications of this work to the study of group actions on binary trees. Comment: Improvements to the introduction. To appear in Fundamenta Mathematicae |
| Databáze: | OpenAIRE |
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