On hyperbolic dimension gap for entire functions

Mayer, Volker; Urbański, Mariusz

Document type :

Pré-publication ou Document de travail

Title :

On hyperbolic dimension gap for entire functions

Author(s) :

Mayer, Volker [Auteur]

Université de Lille
Urbański, Mariusz [Auteur]
University of North Texas [UNT]

Publication date :

2023-07-21

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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 ...
Show more >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 $\HypDim(f)<\HD(\J_f)$.Show less >

Language :

Anglais

Comment :

15 pages

Collections :