We introduce a new concept of interval rearrangement ensembles (IRE), which is a generalization of interval exchange transformations (IET). This construction extends the space of IETs in accordance with the pinpointed natural duality. Induction of Rauzy–Veech kind is applicable to IREs. It is conjugate to the reverse operation by the duality mentioned above. A natural extension of an IRE is associated with two transverse flows on a flat translation surface with branching points.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 2, pp. 247–268, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.6341.
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Teplinsky, A. Interval Rearrangement Ensembles. Ukr Math J 75, 282–304 (2023). https://doi.org/10.1007/s11253-023-02199-2
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DOI: https://doi.org/10.1007/s11253-023-02199-2