Interval rearrangement ensembles - Teplinsky, A. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.5We 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.