2011/10/11 by Jon Chaika, Chaika, Jon, Vaibhav Gadre +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1110.2474
A natural generalization of interval exchange maps are linear involutions,\nfirst introduced by Danthony and Nogueira. Recurrent train tracks with a single\nswitch which we call non-classical interval exchanges, form a subclass of\nlinear involutions without flips. They are analogs of classical interval\nexchanges, and are first return maps for non-orientable measured foliations\nassociated to quadratic differentials on Riemann surfaces. We show that every\ntransformation is disjoint from almost every irreducible non-classical interval\nexchange. In the appendix, we prove that for almost every pair of quadratic\ndifferentials with respect to the Masur-Veech measure, the vertical flows are\ndisjoint. In the appendix, we prove that for almost every pair of quadratic\ndifferentials with respect to the Masur-Veech measure, the vertical flows are\ndisjoint.\n