Multifractal analysis of homological growth rates for hyperbolic surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909486261731328 |
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| author | Jaerisch, Johannes Takahasi, Hiroki |
| author_facet | Jaerisch, Johannes Takahasi, Hiroki |
| contents | We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08907 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multifractal analysis of homological growth rates for hyperbolic surfaces Jaerisch, Johannes Takahasi, Hiroki Dynamical Systems We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum. |
| title | Multifractal analysis of homological growth rates for hyperbolic surfaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2204.08907 |