On Gibbs measures for almost additive sequences associated to some relative pressure functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915850690232320 |
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| author | Yayama, Yuki |
| author_facet | Yayama, Yuki |
| contents | 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 $\lim_{n\to\infty}\frac{1}{n}\int \log f_n dμ=\int f dμ$ 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 $\mathcal{F}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Gibbs measures for almost additive sequences associated to some relative pressure functions Yayama, Yuki Dynamical Systems 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 $\lim_{n\to\infty}\frac{1}{n}\int \log f_n dμ=\int f dμ$ 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 $\mathcal{F}$ 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. |
| title | On Gibbs measures for almost additive sequences associated to some relative pressure functions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2402.10199 |