Ruelle's zeta function for non-Archimedean rational maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912924818210816 |
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| author | Jiang, Yunping Wu, Chenxi |
| author_facet | Jiang, Yunping Wu, Chenxi |
| contents | We studied the transfer operators defined over $\mathbb{C}_p$-valued analytic functions for subhyperbolic rational maps on $\mathbb{Q}_p$, and showed that the corresponding Ruelle's zeta functions are meromorphic on $\mathbb{C}_p$. We also used $\mathbb{R}$-valued transfer operators to study the shape of the corresponding Julia sets, and proved a Levin-Sodin-Yuditski type identity for general rational maps on $\mathbb{C}_p$. In all the results above, $\mathbb{Q}_p$ can be replaced with any non-Archimedean local field with characteristic $0$, and $\mathbb{C}_p$ the metric completion of its algebraic closure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ruelle's zeta function for non-Archimedean rational maps Jiang, Yunping Wu, Chenxi Dynamical Systems Functional Analysis Number Theory 37P05, 37P20, 37D35, 37P10, 11S82, 37P40 We studied the transfer operators defined over $\mathbb{C}_p$-valued analytic functions for subhyperbolic rational maps on $\mathbb{Q}_p$, and showed that the corresponding Ruelle's zeta functions are meromorphic on $\mathbb{C}_p$. We also used $\mathbb{R}$-valued transfer operators to study the shape of the corresponding Julia sets, and proved a Levin-Sodin-Yuditski type identity for general rational maps on $\mathbb{C}_p$. In all the results above, $\mathbb{Q}_p$ can be replaced with any non-Archimedean local field with characteristic $0$, and $\mathbb{C}_p$ the metric completion of its algebraic closure. |
| title | Ruelle's zeta function for non-Archimedean rational maps |
| topic | Dynamical Systems Functional Analysis Number Theory 37P05, 37P20, 37D35, 37P10, 11S82, 37P40 |
| url | https://arxiv.org/abs/2508.19374 |