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Detailed view Article in peer-reviewed journal
Topology and Applications 66 (1995) 171-183
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Foliations of surfaces and semi-Markovian subsets of subshifts of finite type.
Athanase Papadopoulos1

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.
1:  IRMA - Institut de Recherche Mathématique Avancée