Finiteness of gibbs measures on noncompact manifolds with pinched negative curvature

2016/10/11 by Barbara Schapira, Schapira, Barbara, Vincent Pit +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1610.03255

openalex publication_date 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the finiteness of Gibbs measures for geodesic flows on negatively curved manifolds by several criteria, analogous to those proposed by Sarig for symbolic dynamical systems over an infinite alphabet. As an application, we recover Dal'bo-Otal-Peigné criterion of finiteness for the Bowen-Margulis measure on geometrically finite hyperbolic manifolds, as well as Peigné' examples of gemetrically infinite manifolds having a finite Bowen-Margulis measure. These criteria should be useful in the future to find more examples with finite Gibbs measures.

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