Counting prime orbits in shrinking intervals for expanding Thurston maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908679637303296 |
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| author | Li, Zhiqiang Shi, Xianghui |
| author_facet | Li, Zhiqiang Shi, Xianghui |
| contents | We establish a local central limit theorem for primitive periodic orbits of expanding Thurston maps, providing a fine-scale refinement of the Prime Orbit Theorem in the context of non-uniformly expanding dynamics. Specifically, we count the number of primitive periodic orbits whose Birkhoff sums for a given potential lie within a family of shrinking intervals. For eventually positive, real-valued \holder continuous potentials that satisfy the strong non-integrability condition, we derive precise asymptotic estimates. In particular, our results apply to postcritically-finite rational maps whose Julia set is the whole Riemann sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting prime orbits in shrinking intervals for expanding Thurston maps Li, Zhiqiang Shi, Xianghui Dynamical Systems Complex Variables Primary: 37D20, Secondary: 37C25, 37C35, 37D35, 57M12 We establish a local central limit theorem for primitive periodic orbits of expanding Thurston maps, providing a fine-scale refinement of the Prime Orbit Theorem in the context of non-uniformly expanding dynamics. Specifically, we count the number of primitive periodic orbits whose Birkhoff sums for a given potential lie within a family of shrinking intervals. For eventually positive, real-valued \holder continuous potentials that satisfy the strong non-integrability condition, we derive precise asymptotic estimates. In particular, our results apply to postcritically-finite rational maps whose Julia set is the whole Riemann sphere. |
| title | Counting prime orbits in shrinking intervals for expanding Thurston maps |
| topic | Dynamical Systems Complex Variables Primary: 37D20, Secondary: 37C25, 37C35, 37D35, 57M12 |
| url | https://arxiv.org/abs/2511.22601 |