Geometriae Dedicata

, Volume 173, Issue 1, pp 105–127 | Cite as

Every transformation is disjoint from almost every non-classical exchange

  • Jon Chaika
  • Vaibhav Gadre
Original Paper


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.


Interval exchange Teichmüller theory Ergodic theory 

Mathematics Subject Classification (2010)

37E05 30F60 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.IAS and Mathematics InstituteUniversity of WarwickCoventryUK

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