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On Gibbs measures for almost additive sequences associated to some relative pressure functions
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 46 / Issue 4 / April 2026
- Published online by Cambridge University Press:
- 22 January 2026, pp. 1106-1124
- Print publication:
- April 2026
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- Article
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Given a weakly almost additive sequence of continuous functions with bounded variation
${\mathcal {F}}=\{\log f_n\}_{n=1}^{\infty }$ on a subshift X over finitely many symbols, we study properties of a function f on X such that 
$\lim _{n\to \infty }({1}/{n})\int \log f_n\,d\mu =\int f\,d\mu $ for every invariant measure 
$\mu $ on X. Under some conditions, we construct a function f on X explicitly, and study a relation between the property of 
${\mathcal {F}}$ 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.
