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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Interval_exchanges_admissibility_and_bra.pdf (352.82 Ko)
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1305.0120v3.pdf (352.82 Ko)
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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
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