Higher-dimensional multifractal analysis for the cusp winding process on hyperbolic surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917204248756224 |
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| author | Arima, Yuya |
| author_facet | Arima, Yuya |
| contents | We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with $m \geq 1$ cusps. Our main theorem establishes a conditional variational principle for the Hausdorff dimension spectrum of the multi-cusp winding process. Moreover, we show that the dimension spectrum defined on $\mathbb{R}_{>0}^m$ is real analytic. To prove the main theorem we use a countable Markov shift with a finitely primitive transition matrix and thermodynamic formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional multifractal analysis for the cusp winding process on hyperbolic surfaces Arima, Yuya Dynamical Systems Number Theory We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with $m \geq 1$ cusps. Our main theorem establishes a conditional variational principle for the Hausdorff dimension spectrum of the multi-cusp winding process. Moreover, we show that the dimension spectrum defined on $\mathbb{R}_{>0}^m$ is real analytic. To prove the main theorem we use a countable Markov shift with a finitely primitive transition matrix and thermodynamic formalism. |
| title | Higher-dimensional multifractal analysis for the cusp winding process on hyperbolic surfaces |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2402.16418 |