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- W2963398117 abstract "Let $T$ be an $m$-interval exchange transformation. By the rank of $T$ we mean the dimension of the $mathbb{Q}$-vector space spanned by the lengths of the exchanged intervals. We prove that if $T$ is minimal and the rank of $T$ is greater than $1+lfloor m/2 rfloor$, then $T$ cannot be written as a power of another interval exchange. We also demonstrate that this estimate on the rank cannot be improved.In the case that $T$ is a minimal 3-interval exchange transformation, we prove a stronger result: $T$ cannot be written as a power of another interval exchange if and only if $T$ satisfies Keane's infinite distinct orbit condition. In the course of proving this result, we give a classification (up to conjugacy) of those minimal interval exchange transformations whose discontinuities all belong to a single orbit." @default.
- W2963398117 created "2019-07-30" @default.
- W2963398117 creator A5063788650 @default.
- W2963398117 date "2017-01-01" @default.
- W2963398117 modified "2023-10-18" @default.
- W2963398117 title "Most interval exchanges have no roots" @default.
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- W2963398117 doi "https://doi.org/10.3934/jmd.2017011" @default.
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