Every transformation is disjoint from almost every non-classical exchange
Abstract
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, 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. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2011
- DOI:
- arXiv:
- arXiv:1110.2474
- Bibcode:
- 2011arXiv1110.2474C
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Dynamical Systems;
- 37E05;
- 30F60
- E-Print:
- Added the appendix