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Deformations of Anosov flows and of Fuchsian groups. (Déformations de flots d’Anosov et de groupes fuchsiens.) (French) Zbl 0759.58036
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.
Reviewer: E.Ghys (Lyon)

MSC:
37D99 Dynamical systems with hyperbolic behavior
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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