FINITENESS OF GIBBS MEASURES ON NONCOMPACT MANIFOLDS WITH PINCHED NEGATIVE CURVATURE

Autor(es)

Pit, Vincent ^[1] ; Schapira, Barbara ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio de Janeiro, Inst Matemat, Ctr Tecnol, Av Athos da Silveira Ramos 149, Bloco C, Rio de Janeiro, RJ - Brazil

^[2] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes - France

• Tipo de documento: Artigo Científico
• Fonte: ANNALES DE L INSTITUT FOURIER; v. 68, n. 2, p. 457-510, 2018.
• Citações Web of Science: 1

Resumo

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. These criteria should be useful in the future to find more examples with finite Gibbs measures. As an application, we recover Dal'bo-Otal-Peigne criterion of finiteness for the Bowen-Margulis measure on geometrically finite hyperbolic manifolds, as well as Peigne's examples of geometrically infinite manifolds having a finite Bowen-Margulis measure. (AU)

• Processo FAPESP: 11/12338-0 - Transformação de Bowen-Series e formalismo termodinâmico para superfícies hiperbólicas de volume finito
• Beneficiário: Vincent Pit
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado