Propriétés ergodiques du feuilletage horosphérique d'une variété à courbure négative

Abstract : In this work, we study the ergodic properties of the horospherical foliation of a geometrically finite negatively curved manifold $M$. One of our main results is the classification of quasi-invariant transverse measures whose Radon-Nokodym derivative is a fixed Hölder cocycle, associated with a Gibbs measure. To such a cocycle we associate certain horospherical means and we prove their equidistribution to the corresponding Gibbs measure when $M$ is compact or convex-cocompact. When $M$ is neither compact nor convex-cocompact, we restrict the study to the means associated with the measure of maximal entropy. We show that they do not diverge; in the case of surfaces, it allows us to prove their equidistribution to the measure of maximal entropy. As a corollary, we get the equidistribution of the orbits of the horocyclic flow of a geometrically finite hyperbolic surface with infinite volume.
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Contributor : Barbara Schapira <>
Submitted on : Tuesday, July 17, 2007 - 2:46:22 PM
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• HAL Id : tel-00163420, version 1

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Barbara Schapira. Propriétés ergodiques du feuilletage horosphérique d'une variété à courbure négative. Mathématiques [math]. Université d'Orléans, 2003. Français. ⟨tel-00163420⟩

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