Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908626735595520 |
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| author | Arima, Yuya |
| author_facet | Arima, Yuya |
| contents | In this paper, we study the multifractal spectrum of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches. Our main theorem substantially strengthens conditional variational formulas established by Jaerisch and Takahasi. Furthermore, our results enable a detailed analysis of Khinchin exponents and arithmetic means of backward continued fraction expansions in terms of the Hausdorff dimension. We also give a positive answer to the conjecture of Jaerisch and Takahasi. In addition, we develop the thermodynamic formalism for non-uniformly expanding Rényi interval maps with countably many branches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02266 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches Arima, Yuya Dynamical Systems In this paper, we study the multifractal spectrum of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches. Our main theorem substantially strengthens conditional variational formulas established by Jaerisch and Takahasi. Furthermore, our results enable a detailed analysis of Khinchin exponents and arithmetic means of backward continued fraction expansions in terms of the Hausdorff dimension. We also give a positive answer to the conjecture of Jaerisch and Takahasi. In addition, we develop the thermodynamic formalism for non-uniformly expanding Rényi interval maps with countably many branches. |
| title | Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.02266 |