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arXiv · 2010.16389

Interval Rearrangement Ensembles

Alexey Teplinsky
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Abstract

We introduce a new concept of interval rearrangement ensembles (IRE), which is a generalization of interval exchange transformations (IET). This construction expands the space of IETs in accordance with the natural duality that we pinpoint. 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 transversal flows on a flat translation surface with branching points.

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Alexey Teplinsky. 2020-10-30. Interval Rearrangement Ensembles. https://doi.org/10.1007/s11253-023-02199-2

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