Equilibrium states in negative curvature

2012/11/27 by Frédéric Paulin, Paulin, Frédéric, Mark Pollicott +3 · 1 citation
Mathematics · #37A25 #37C35 #37D35 #37D40 #53C12 #53D25 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.1211.6242

openalex publication_date 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. We give many applications, to the Variational Principle, the counting and equidistribution of orbit points and periods, the unique ergodicity of the strong unstable foliation and the classification of Gibbs densities on some Riemannian covers.

Cited by

• Counting and equidistribution of strongly reversible closed geodesics in negative curvature

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