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Whirly 3-interval exchange transformations

Published online by Cambridge University Press:  20 October 2015

YUE WU
YUE WU*
Affiliation:
3519 Heartland Key LN, Katy, TX 77494, USA email wuuyue@gmail.com Schlumberger PTS Full Waveform Inversion Center of Excellence, Houston, TX, USA
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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 $m\geq 4$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 3 , May 2017 , pp. 995 - 1008
Copyright
© Cambridge University Press, 2015 

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