Finiteness of gibbs measures on noncompact manifolds with pinched negative curvature

Barbara Schapira (IRMAR); Vincent Pit (UFRJ)

arxiv: 1610.03255 · v1 · pith:BRIOB4LJnew · submitted 2016-10-11 · 🧮 math.DS

Finiteness of gibbs measures on noncompact manifolds with pinched negative curvature

Barbara Schapira (IRMAR) , Vincent Pit (UFRJ) This is my paper

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keywords manifoldsfinitefinitenessgibbsmeasuresbowen-marguliscriteriaexamples

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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-Peign{\'e} criterion of finiteness for the Bowen-Margulis measure on geometrically finite hyperbolic manifolds, as well as Peign{\'e}' 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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