We study Anosov flows on compact 3-manifolds for which weak stable and unstable distributions are . 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.
Nous étudions les flots d’Anosov sur les variétés compactes de dimension 3 pour lesquels les distributions stable et instable faibles sont de classe . 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.
@article{AIF_1992__42_1-2_209_0, author = {Ghys, \'Etienne}, title = {D\'eformations de flots {d'Anosov} et de groupes fuchsiens}, journal = {Annales de l'Institut Fourier}, pages = {209--247}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {1-2}, year = {1992}, doi = {10.5802/aif.1290}, zbl = {0759.58036}, mrnumber = {93j:58111}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1290/} }
TY - JOUR AU - Ghys, Étienne TI - Déformations de flots d'Anosov et de groupes fuchsiens JO - Annales de l'Institut Fourier PY - 1992 SP - 209 EP - 247 VL - 42 IS - 1-2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1290/ DO - 10.5802/aif.1290 LA - fr ID - AIF_1992__42_1-2_209_0 ER -
%0 Journal Article %A Ghys, Étienne %T Déformations de flots d'Anosov et de groupes fuchsiens %J Annales de l'Institut Fourier %D 1992 %P 209-247 %V 42 %N 1-2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1290/ %R 10.5802/aif.1290 %G fr %F AIF_1992__42_1-2_209_0
Ghys, Étienne. Déformations de flots d'Anosov et de groupes fuchsiens. Annales de l'Institut Fourier, Volume 42 (1992) no. 1-2, pp. 209-247. doi : 10.5802/aif.1290. https://aif.centre-mersenne.org/articles/10.5802/aif.1290/
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