On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold

2002/07/04 by Barbara Schapira, Schapira, Barbara
Mathematics · #22F05 #37A20 #37C85 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.DS #msc:22F05 #msc:37A20 #msc:37C85 #msc:37D40

paper · pdf · doi:10.48550/arxiv.math/0207043

28 pages, 6 figures

arxiv created 2002/07/04 · openalex publication_date 2002/07/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If M is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on \tm a quasi-invariant transverse measure for the horospherical foliation, and prove that this measure is uniquely determined by its Radon-Nikodym cocycle. (This extends the Bowen-Marcus unique ergodicity result for this foliation.) We shall also prove equidistribution properties for the leaves of the foliation w.r.t. these Gibbs measures. We use these results in the study of invaiant meausres for horospherical foliations on regular covers of M.

Related

• Gibbs measures for foliated bundles with negatively curved leaves
• Horospherical dynamics in invariant subvarieties
• Gibbs u-states for the foliated geodesic flow and transverse invariant\n measures
• Physical measures for the geodesic flow tangent to a transversally conformal foliation
• Equilibrium states in negative curvature