no. 3
Topologie du feuilletage fortement stable
Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 981-993.

Soient X une variété de Hadamard de courbure ≤-1 et Γ un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de Γ∖X, le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.

Let X be a Hadamard manifold with curvature ≤-1 and Γ be a non elementary isometry group acting freely properly discontinuously on X. We are interested in the topology of the leaves of the strong stable foliation ℱ on T 1 (Γ∖X). We establish equivalences between the non arithmeticity of Γ (i.e. the group generated by the length spectrum of Γ∖X is dense in ℝ), the existence of a dense leaf in the non wandering set Ω X of ℱ and the topological mixing of the geodesic flow on its non wandering set. Our proof uses the action of Γ on X(∞) and the relation between cross-ratio and length spectrum.In the case when Γ is not arithmetic, we prove that Γ is geometrically finite if and only if leaves in Ω X are dense or are associated to bounded parabolic fixed points (such leaves are closed).

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     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},
     zbl = {0965.53054},
     mrnumber = {2001i:37045},
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Dal'bo, Françoise. Topologie du feuilletage fortement stable. Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 981-993. doi : 10.5802/aif.1781. https://aif.centre-mersenne.org/articles/10.5802/aif.1781/

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