A characterization of pseudo-Anosov foliations
Let M be a closed oriented smooth surface of genus at least two. We address the problem of recognizing when an equivalence class of measured foliations on M is left invariant by some pseudo-Anosov map of M. Our solution to this problem is essentially combinatorial. Using train tracks, we associate a semi-infinite word in a finite alphabet to a class of measured foliations. Roughly, it is proved that a measured foliation class is invariant under a pseudo-Anosov map if and only if it admits an eventually periodic combinatorial word. The proof is in some sense constructive, and an algorithm for generating all conjugacy classes of pseudo-Anosov maps is described.
scientific article; zbMATH DE number 3971785
scientific article