Foliations of surfaces and semi-Markovian subsets of subshifts of finite type
A space \(\mathcal F\) of equivalence classes of measured foliations of a closed surface \(S\) of genus \(g\geq 2\) is defined as the quotient space of Thurston measured foliation space. \({\mathcal M}{\mathcal F}\) by the equivalence relation identifying two elements of \({\mathcal M}{\mathcal F}\) if they can be presented by measured foliations on the surface which agree as foliations, regardless of the transverse measure. It is given the presentation (in the sense of symbolic dynamics) of the action of a pseudo-Anosov mapping class of \(\mathcal M\) in the neighborhood of its attracting fixed point in \(\mathcal F\). It is stated that the action is semi-Markovian.
scientific article; zbMATH DE number 823478
scientific article