Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimension
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911854292369408 |
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| author | Esparza-Amador, Adrián |
| author_facet | Esparza-Amador, Adrián |
| contents | We consider the family of entire maps given by $f_{\ell,c}(z)=\ell+c-(\ell-1)\log c-e^z$, where $c\in D(\ell,1)$ and $\ell\in\mathbb N$, $\ell\geq2$. By using the property of $f_{\ell,c}$ to be dynamically projected to an infinite cylinder $\mathbb C/2πI\mathbb Z$, where the thermodynamic formalism tools are well-defined, we prove as a main result on this work, the real-analyticity of the map $c\mapsto HD(\mathcal{J}_r(f_{\ell,c}))$, here $\mathcal{J}_r(f_{\ell,c})$ is the radial Julia set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimension Esparza-Amador, Adrián Dynamical Systems 37F10, 37D35, 37F35 We consider the family of entire maps given by $f_{\ell,c}(z)=\ell+c-(\ell-1)\log c-e^z$, where $c\in D(\ell,1)$ and $\ell\in\mathbb N$, $\ell\geq2$. By using the property of $f_{\ell,c}$ to be dynamically projected to an infinite cylinder $\mathbb C/2πI\mathbb Z$, where the thermodynamic formalism tools are well-defined, we prove as a main result on this work, the real-analyticity of the map $c\mapsto HD(\mathcal{J}_r(f_{\ell,c}))$, here $\mathcal{J}_r(f_{\ell,c})$ is the radial Julia set. |
| title | Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimension |
| topic | Dynamical Systems 37F10, 37D35, 37F35 |
| url | https://arxiv.org/abs/2404.17076 |