Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912170909892608 |
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| author | Li, Zhiqiang Zheng, Tianyi |
| author_facet | Li, Zhiqiang Zheng, Tianyi |
| contents | In the second paper [LZ24b] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In this third and last paper of the series, we show that the $α$-strong non-integrability condition is generic in the class of $α$-Hölder continuous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06687 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition Li, Zhiqiang Zheng, Tianyi Dynamical Systems Complex Variables Primary: 37C30, Secondary: 37C35, 37F15, 37B05, 37D35 In the second paper [LZ24b] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In this third and last paper of the series, we show that the $α$-strong non-integrability condition is generic in the class of $α$-Hölder continuous functions. |
| title | Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition |
| topic | Dynamical Systems Complex Variables Primary: 37C30, Secondary: 37C35, 37F15, 37B05, 37D35 |
| url | https://arxiv.org/abs/2312.06687 |