Search results for "Mesures de Gibbs"

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Gibbs and harmonic measures for foliations with negatively curved leaves

2013

Pas de résumé en anglais.

[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Mesures de GibbsGibbs
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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.

Feuilletages[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]théorie ergodiqueMathematics::Differential Geometryactions de groupesMesures de GibbsGibbs
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