Computations on the transverse measured foliations associated with a pseudo-Anosov automorphism (Q1327445)

Let \(g\) be a pseudo-Anosov diffeomorphism of a compact surface \(S\) of genus \(p\), \(p>1\). The author makes a partition of the lift of the unstable foliation \(\Phi_ U\) associated with \(g\) to the universal covering space (the unit disk \(U\)) into a countable number of layers approximating inaccessible points for \(\Phi_ U\) at infinity. The regular step lines are studied, which are similar to geodesics on a surface. For example, the regular step line through two points \(z_ 0\) and \(z\) on \(S\) minimizes the total variation in a homotopy class of curves with fixed points at \(z_ 0\) and \(z\). Formulas for computing the fixed points for \(g\) and its lift are obtained in terms of regular step lines.