On Gibbs measures for almost additive sequences associated to some relative pressure functions

2024/02/15 by Yayama, Yuki
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.10199

Abstract

Given a weakly almost additive sequence of continuous functions with bounded variation F=\log f_n\_n=1^∞ on a subshift X over finitely many symbols, we study properties of a function f on X such that lim_n→∞(1)/(n)∫ log f_n dμ=∫ f dμ for every invariant measure μ on X. Under some conditions we construct a function f on X explicitly and study a relation between the property of F and some particular types of f. As applications we study images of Gibbs measures for continuous functions under one-block factor maps. We investigate a relation between the almost additivity of the sequences associated to relative pressure functions and the fiber-wise sub-positive mixing property of a factor map. For a special type of one-block factor maps between shifts of finite type, we study necessary and sufficient conditions for the image of a one-step Markov measure to be a Gibbs measure for a continuous function.

Related

• Relative pressure functions and their equilibrium states
• The Pressure Function for Products of Non-negative Matrices
• Pressure Inequalities for Gibbs Measures of Countable Markov Shifts
• On the superadditive pressure for 1-typical, one-step, matrix-cocycle potentials
• On the preservation of Gibbsianness under symbol amalgamation