Sequential Gibbs Measures and Factor Maps

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.