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Journal of Statistical Physics

, Volume 172, Issue 3, pp 833–853 | Cite as

Sequential Gibbs Measures and Factor Maps

  • Giovane Ferreira
  • Krerley Oliveira
Article

Abstract

We define the notion of sequential Gibbs measures, inspired by on the classical notion of Gibbs measures and recent examples from the study of non-uniform hyperbolic dynamics. Extending previous results of Kempton and Pollicott (Factors of Gibbs measures for full shifts, entropy of hidden Markov processes and connections to dynamical systems, Cambridge University Press, Cambridge, 2011) and Chazottes and Ugalde (On the preservation of Gibbsianness under symbol amalgamation, entropy of hidden Markov processes and connections to dynamical systems, Cambridge University Press, Cambridge, 2011), we show that the images of one block factor maps of a sequential Gibbs measure are also a sequential Gibbs measure, with the same sequence of Gibbs times. We obtain some estimates on the regularity of the potential of the image measure at almost every point.

Keywords

Full shift Sequential Gibbs measure Factor maps Equilibrium states Thermodynamic formalism Regularity of the potential 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidade Federal do MaranhãoSão LuísBrazil
  2. 2.Universidade Federal de AlagoasMaceióBrazil

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