Harmonic measures and the foliated geodesic flow for foliations with negatively curved leaves

Sébastien Alvarez (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

In this paper we define a notion of Gibbs measure for the geodesic flow tangent to a foliation with negatively curved leaves and associated to a particular potential $H$. We prove that there is a canonical bijective correspondence between these measures and Garnett's harmonic measures.

Mots clés: Curvature; Laminations

Domaines: Systèmes dynamiques [math.DS]

Sébastien Alvarez. Harmonic measures and the foliated geodesic flow for foliations with negatively curved leaves. Ergodic Theory and Dynamical Systems, 2016, 36 (2), pp.355 - 374. ⟨10.1017/etds.2014.59⟩. ⟨hal-01413451⟩