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

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.

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Bibliographic Details
Published in:arXiv.org 2021-12
Main Author: Przytycki, Feliks
Format: Article
Language:English
Subjects:
Approximation
Hyperbolic functions
Rational functions
Riemann manifold
Online Access:Get full text
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Summary: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.
ISSN:2331-8422