Ротаційні перекладання інтервалів

A. Teplinsky

doi:10.3842/umzh.v76i3.7779

A. Teplinsky Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv

DOI: https://doi.org/10.3842/umzh.v76i3.7779

Keywords: circle rotation, interval exchange transformation, interval rearrangement ensemble, duality

Abstract

UDC 517.5

We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first definition, it is the first return map for a circle rotation onto a union of finitely many circle arcs and, by the second definition, it is an interval exchange with a scheme (in the sense of interval rearrangement ensembles) whose dual is also an interval exchange scheme.

References

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Rotational interval exchange transformations

Abstract

References