Interval exchanges, admissibility and branching Rauzy induction

Abstract : We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular interval exchange set is a regular interval exchange set with the same number of intervals. Derivation is taken here with respect to return words. We characterize the admissible intervals using a branching version of the Rauzy induction. We also study the case of regular interval exchange transformations defined over a quadratic field and show that the set of factors of such a transformation is primitive morphic. The proof uses an extension of a result of Boshernitzan and Carroll.
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Contributor : Francesco Dolce <>
Submitted on : Friday, September 16, 2016 - 3:37:00 PM
Last modification on : Thursday, July 5, 2018 - 2:45:48 PM
Long-term archiving on : Saturday, December 17, 2016 - 2:49:17 PM

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Francesco Dolce, Dominique Perrin. Interval exchanges, admissibility and branching Rauzy induction. 2016. ⟨hal-01367715⟩

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