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arXiv · 2511.02266

Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding R\'{e}nyi interval maps with countably many branches

Yuya Arima
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Abstract

In this paper, we study the multifractal spectrum of Birkhoff averages for non-uniformly expanding R\'{e}nyi 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 R\'{e}nyi interval maps with countably many branches.

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Yuya Arima. 2025-11-04. Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding R\'{e}nyi interval maps with countably many branches. https://arxiv.org/abs/2511.02266

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