Search results for "feuilletages"
showing 4 items of 4 documents
Gibbs and harmonic measures for foliations with negatively curved leaves
2013
In this thesis we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of F-harmonic measure and prove that there exists a natural bijective correspondence between the two. For projective foliated bundles with sphere-fibers without transverse invariant measure, we show the uniqueness of these measures for any Hölder potential on the basis. In that case we also prove that F-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that their conditional measures on the fibers are limits of weighted averages on the orbits of the holonomy group.
Partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy
2011
The thesis classifies partially hyperbolic diffeomorphisms with a compact center foliation with finite holonomy. Under the further assumption of a one-dimensional unstable bundle we show the following: If the unstable bundle is oriented then the system fibers over a hyperbolic toral automorphism. We further establish that the system has a dense orbit of center leaves. During the proof we show a Shadowing Lemma and the dynamical coherence without restrictions of the dimensions.
Volumes transverses aux feuilletages d'efinissables dans des structures o-minimales
2003
Let Fλ be a family of codimension p foliations defined on a family Mλ of manifolds and let Xλ be a family of compact subsets of Mλ. Suppose that Fλ, Mλ and Xλ are definable in an o-minimal structure and that all leaves of Fλ are closed. Given a definable family Ωλ of differential p-forms satisfaying iZ Ωλ = 0 forany vector field Z tangent to Fλ, we prove that there exists a constant A > 0 such that the integral of on any transversal of Fλ intersecting each leaf in at most one point is bounded by A. We apply this result to prove that p-volumes of transverse sections of Fλ are uniformly bounded.
Integral geometry from Buffon to geometers of today
2016
La géométrie intégrale, aussi appelée théorie des probabilités géométriques, a accompagné pendant plus de deux siècles le développement des probabilités, de la théorie de la mesure et de la géométrie. Elle commence pour nous en 1777, date de la publication du « traité d'arithmétique morale » de Buffon. Ce n'est que presque un siècle plus tard que Crofton explicitera ce que veut dire mettre une mesure sur un ensemble continu comme l'ensemble des droites. Le sens de la formule de Cauchy-Crofton « la longueur d'une courbe plane est proportionnelle à la mesure pondérée de l'ensemble des droites qui la coupent », est maintenant clair. Au début du vingtième siècle, la géométrie intégrale commence…