Weak Gibbs measures for the natural extension of $(κ/β, β)$-shifts
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910022695387136 |
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| author | Yamashita, Miki |
| author_facet | Yamashita, Miki |
| contents | In this paper we consider the weak Gibbs measures for $(α, β)$-shifts. In the case of $α=0$, Pfister and Sullivan have given a necessary and sufficient condition on $β$ such that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure in the natural extension of a $β$-shift. So it is natural to ask what happens when $α>0$. However, their proof cannot be applied to general $(α, β)$-shifts in a similar way. In this paper we consider the case of $α=κ/β$ and give a criterion for the weak Gibbs property of equilibrium measures for $(κ/β, β)$-shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Gibbs measures for the natural extension of $(κ/β, β)$-shifts Yamashita, Miki Dynamical Systems 37B10, 37D35, 28D05 In this paper we consider the weak Gibbs measures for $(α, β)$-shifts. In the case of $α=0$, Pfister and Sullivan have given a necessary and sufficient condition on $β$ such that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure in the natural extension of a $β$-shift. So it is natural to ask what happens when $α>0$. However, their proof cannot be applied to general $(α, β)$-shifts in a similar way. In this paper we consider the case of $α=κ/β$ and give a criterion for the weak Gibbs property of equilibrium measures for $(κ/β, β)$-shifts. |
| title | Weak Gibbs measures for the natural extension of $(κ/β, β)$-shifts |
| topic | Dynamical Systems 37B10, 37D35, 28D05 |
| url | https://arxiv.org/abs/2509.25621 |