Every transformation is disjoint from almost every non-classical exchange

Chaika, J. and Gadre, V. (2014) Every transformation is disjoint from almost every non-classical exchange. Geometriae Dedicata, 173(1), pp. 105-127. (doi: 10.1007/s10711-013-9931-5)

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A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira (Ann Sci École Norm Sup (4) 26(6):645–664, 1993). Recurrent train tracks with a single switch which are called non-classical interval exchanges (Gadre in Ergod Theory Dyn Syst 32(06):1930–1971, 2012), form a subclass of linear involutions without flips. They are analogs of classical interval exchanges, and are first return maps for non-orientable measured foliations associated to quadratic differentials on Riemann surfaces. We show that every transformation is disjoint from almost every irreducible non-classical interval exchange. In the “Appendix”, we prove that for almost every pair of quadratic differentials with respect to the Masur–Veech measure, the vertical flows are disjoint.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Gadre, Dr Vaibhav
Authors: Chaika, J., and Gadre, V.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometriae Dedicata
ISSN (Online):1572-9168
Copyright Holders:Copyright © 2013 Springer-Verlag Berlin Heidelberg
First Published:First published in Geometriae Dedicata 173(1):105-127
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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