Thermodynamic formalism and hyperbolic Baker domains: Real-analyticity of the Hausdorff dimension

2024/04/25 by Esparza-Amador, Adrián
#37D35 #37F10 #37F35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.17076

Abstract

We consider the family of entire maps given by f_ℓ,c(z)=ℓ+c-(ℓ-1)log c-e^z, where c∈ D(ℓ,1) and ℓ∈\mathbb N, ℓ≥2. By using the property of f_ℓ,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↦ HD(J_r(f_ℓ,c)), here J_r(f_ℓ,c) is the radial Julia set.

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