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Number of ergodic transverse measures for geodesic laminations - bounded by the genus?

Foliations - Train Tracks: Calegari talks about this trichotomy in his book Foliations and the geometry of 3-manifolds, and Erlandsson and Souto relate geodesic lamniations to weighted train tracks in … But none of them relate them to interval exchange transformations. -- Katok and other mathematicians discuss the amount of ergodic measures for certain singular foliations in surfaces, but again there …