Let be a Hadamard manifold with curvature and be a non elementary isometry group acting freely properly discontinuously on . We are interested in the topology of the leaves of the strong stable foliation on . We establish equivalences between the non arithmeticity of (i.e. the group generated by the length spectrum of is dense in ), the existence of a dense leaf in the non wandering set of and the topological mixing of the geodesic flow on its non wandering set. Our proof uses the action of on and the relation between cross-ratio and length spectrum.In the case when is not arithmetic, we prove that is geometrically finite if and only if leaves in are dense or are associated to bounded parabolic fixed points (such leaves are closed).
Soient une variété de Hadamard de courbure et un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de , le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.
@article{AIF_2000__50_3_981_0, author = {Dal'bo, Fran\c{c}oise}, title = {Topologie du feuilletage fortement stable}, journal = {Annales de l'Institut Fourier}, pages = {981--993}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {3}, year = {2000}, doi = {10.5802/aif.1781}, mrnumber = {2001i:37045}, zbl = {0965.53054}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1781/} }
TY - JOUR AU - Dal'bo, Françoise TI - Topologie du feuilletage fortement stable JO - Annales de l'Institut Fourier PY - 2000 SP - 981 EP - 993 VL - 50 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1781/ DO - 10.5802/aif.1781 LA - fr ID - AIF_2000__50_3_981_0 ER -
Dal'bo, Françoise. Topologie du feuilletage fortement stable. Annales de l'Institut Fourier, Volume 50 (2000) no. 3, pp. 981-993. doi : 10.5802/aif.1781. http://www.numdam.org/articles/10.5802/aif.1781/
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