McMullen's and geometric pressures and approximating Hausdorff dimension of Julia sets from below

2021/12/24 by Feliks Przytycki, Przytycki, Feliks
Mathematics · Social Sciences · #Dynamical Systems (math.DS) #FOS: Mathematics #Historical Geography and Cartography #Mathematical Dynamics and Fractals #Mathematics and Applications #Primary: 37F35 #Secondary: 37F10

paper · pdf · doi:10.48550/arxiv.2112.13008

openalex publication_date 2021/12/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We introduce new variants of the notion of geometric pressure for rational functions on the Riemann sphere, including non-hyperbolic functions, in the hope some of them occur useful to achieve a fast approximation from below of the hyperbolic Hausdorff dimension of Julia set.

Related

• Hausdorff dimension of Julia sets of unicritical correspondences
• Hausdorff dimension of Julia sets in the logistic family
• The size of the Julia set of meromorphic functions
• The Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps
• Geometric pressure in real and complex 1-dimensional dynamics via trees\n of preimages and via spanning sets