The size of the Julia set of meromorphic functions
Volker Mayer
TL;DR
This paper establishes lower bounds for the hyperbolic and Hausdorff dimensions of Julia sets associated with meromorphic functions of finite order, under broad conditions, advancing understanding of their fractal geometry.
Contribution
It provides new lower bounds for the dimensions of Julia sets of meromorphic functions of finite order, extending previous results to more general settings.
Findings
Lower bounds for hyperbolic dimension
Lower bounds for Hausdorff dimension
Applicable to broad classes of meromorphic functions
Abstract
We give a lower bound of the hyperbolic and the Hausdorff dimension of the Julia set of meromorphic functions of finite order under very general conditions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · advanced mathematical theories