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Topology and Applications 66 (1995) 171-183

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

Athanase Papadopoulos 1

(31/10/1995)

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 :	Institut de Recherche Mathématique Avancée (IRMA)
	CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I

Domaine

:

Mathématiques/Topologie générale

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Soumis le : Jeudi 8 Février 2007, 16:17:25

Dernière modification le : Jeudi 8 Février 2007, 17:14:05