Déformations de flots d'Anosov et de groupes fuchsiens

Ghys, Étienne

Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 209-247.

Nous étudions les flots d’Anosov sur les variétés compactes de dimension 3 pour lesquels les distributions stable et instable faibles sont de classe $C^{\infty }$. Nous classons tous ces flots lorsqu’ils préservent le volume puis nous construisons une famille d’exemples qui ne préservent pas le volume. Nous classons aussi ces flots sous une hypothèse de “pincement”. En application, nous décrivons les déformations des groupes fuchsiens dans le groupe des difféomorphismes du cercle.

We study Anosov flows on compact 3-manifolds for which weak stable and unstable distributions are $C^{\infty }$. We classify these flows if they are volume preserving and we construct a family of examples which are not volume preserving. We also classify these flows under a “pinching" assumption. As an application, we describe deformations of Fuchsian groups in the group of diffeomorphisms of the circle.

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