On hyperbolic dimension gap for entire functions

Volker Mayer; Mariusz Urbański

On hyperbolic dimension gap for entire functions

Dynamical Systems 2023-07-24 v2 Complex Variables

Authors: Volker Mayer , Mariusz Urbański

Abstract

Polynomials and entire functions whose hyperbolic dimension is strictly smaller than the Hausdorff dimension of their Julia set are known to exist but in all these examples the latter dimension is maximal, i.e. equal to two. In this paper we show that there exist hyperbolic entire functions $f$ having Hausdorff dimension of the Julia set $\HD (\J _f)<2$ and hyperbolic dimension $\HypDim(f)<\HD(\J_f)$ .

Keywords

hausdorff dimension hyperbolic geometry julia set

Cite

@article{arxiv.2306.02627,
  title  = {On hyperbolic dimension gap for entire functions},
  author = {Volker Mayer and Mariusz Urbański},
  journal= {arXiv preprint arXiv:2306.02627},
  year   = {2023}
}

Comments

15 pages

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