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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 0046-5755
• 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