Topologie du feuilletage fortement stable

Françoise Dal'bo

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 3, page 981-993
  • ISSN: 0373-0956

Abstract

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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).

How to cite

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Dal'bo, Françoise. "Topologie du feuilletage fortement stable." Annales de l'institut Fourier 50.3 (2000): 981-993. <http://eudml.org/doc/75446>.

@article{Dalbo2000,
abstract = {Soient $X$ une variété de Hadamard de courbure $\le -1$ et $\Gamma $ un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de $\Gamma \backslash X$, le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.},
author = {Dal'bo, Françoise},
journal = {Annales de l'institut Fourier},
keywords = {geodesic flow; foliation; discontinuous isometry group; homogeneous space},
language = {fre},
number = {3},
pages = {981-993},
publisher = {Association des Annales de l'Institut Fourier},
title = {Topologie du feuilletage fortement stable},
url = {http://eudml.org/doc/75446},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Dal'bo, Françoise
TI - Topologie du feuilletage fortement stable
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 3
SP - 981
EP - 993
AB - Soient $X$ une variété de Hadamard de courbure $\le -1$ et $\Gamma $ un groupe d’isométries non élémentaire. Nous montrons qu’il y a équivalence entre la non-arithméticité du spectre des longueurs de $\Gamma \backslash X$, le mélange topologique du flot géodésique et l’existence d’une feuille dense pour le feuilletage fortement stable.
LA - fre
KW - geodesic flow; foliation; discontinuous isometry group; homogeneous space
UR - http://eudml.org/doc/75446
ER -

References

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