Foliations of surfaces and semi-Markovian subsets of subshifts of finite type.

Athanase Papadopoulos (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Let $S$ be a closed surface of genus $ggeq 2$. In this paper, we consider a space, which we call ${cal F}$, of equivalence classes of measured foliations of $S$, defined as the quotient of Thurston's measured foliation space where one forgets the transverse measure associated to a measured foliation. We give a presentation, in the sense of symbolic dynamics, of the action of a pseudo-Anosov mapping class of $M$ in the neighborhood of its attracting fixed point in ${cal F}$. The action is semi-Markovian. The elements of the combinatorics associated to the presentation consist in an invariant train track with a marking on its set of vertices and a certain number of elementary moves on it.

Domaines: Topologie générale [math.GN]

Athanase Papadopoulos. Foliations of surfaces and semi-Markovian subsets of subshifts of finite type.. Topology and Applications, 1995, 66, pp.171-183. ⟨hal-00129540⟩