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Weak Gibbs measures as Gibbs measures for asymptotically additive sequences


Authors: Godofredo Iommi and Yuki Yayama
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 37D35, 37D25
Published electronically: September 30, 2016
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Abstract: In this note we prove that every weak Gibbs measure for an asymptotically additive sequence is a Gibbs measure for another asymptotically additive sequence. In particular, a weak Gibbs measure for a continuous potential is a Gibbs measure for an asymptotically additive sequence. This allows us, for example, to apply recent results on dimension theory of asymptotically additive sequences to study multifractal analysis for weak Gibbs measure for continuous potentials.


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Godofredo Iommi
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Chile
Email: giommi@mat.puc.cl

Yuki Yayama
Affiliation: Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Departamento de Ciencias Básicas, Universidad del Bío-Bío, Avenida Andrés Bello, s/n Casilla 447, Chillán, Chile
Email: yyayama@ubiobio.cl

DOI: https://doi.org/10.1090/proc/13311
Keywords: Thermodynamic formalism, weak Gibbs measures, asymptotically additive sequences
Received by editor(s): May 12, 2015
Received by editor(s) in revised form: March 16, 2016, and May 26, 2016
Published electronically: September 30, 2016
Additional Notes: Both authors were supported by the Center of Dynamical Systems and Related Fields código ACT1103 PIA - Conicyt. The first author was partially supported by Proyecto Fondecyt 1150058.
The second author was supported by Proyecto Fondecyt 1151368 y Grupo de Investigación GI 151008/VC at Universidad del Bío-Bío.
Communicated by: Nimish Shah
Article copyright: © Copyright 2016 American Mathematical Society