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Mathematics > Dynamical Systems
Title: Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimension
(Submitted on 25 Apr 2024)
Abstract: 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 $\mathbb C/2\pi I\mathbb Z$, 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.
Submission history
From: Adrián Esparza-Amador [view email][v1] Thu, 25 Apr 2024 23:01:09 GMT (20kb)
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