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La notion de type géométrique d’une partition de Markov est au centre de la
classification des difféomorphismes de Smale i.e. des difféomorphismes -
structurellement stables des surfaces. On résout ici le problème de réalisabilité : on
donne un critère effectif pour décider si une combinatoire abstraite est, ou n’est pas,
le type géométrique d’une partition de Markov de pièce basique de difféomorphisme de
Smale de surface compacte.
Michael Handel proved the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel's theorem to a wider class of cycles of links. In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.
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