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Whirly 3-interval exchange transformations
Published online by Cambridge University Press: 20 October 2015
Abstract
Irreducible interval exchange transformations are studied with regard to the whirly property, a condition for a non-trivial spatial factor. A uniformly whirly transformation is defined and is further studied. An equivalent condition is introduced for the whirly transformation. We will prove that almost all 3-interval exchange transformations are whirly, using a combinatorics approach with application of the Rauzy–Veech induction. It is still an open question whether the whirly property is a generic property for $m$-interval exchange transformations for $m\geq 4$.
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- © Cambridge University Press, 2015