Titre :

The exact value of Hausdorff dimension of escaping sets of class $${\mathcal {B}}$$ meromorphic functions

Auteur(s) :

Mayer, Volker [Auteur]
Université de Lille
Urbański, Mariusz [Auteur]

Titre de la revue :

Geometric And Functional Analysis

Pagination :

53-80

Éditeur :

Springer Verlag

Date de publication :

2022-01-25

ISSN :

1016-443X

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

We consider the subclass of class B consisting of meromorphic functions f : C → C for which infinity is not an asymptotic value and whose all poles have orders uniformly bounded from above. This class was introduced in [7] ...
Lire la suite >We consider the subclass of class B consisting of meromorphic functions f : C → C for which infinity is not an asymptotic value and whose all poles have orders uniformly bounded from above. This class was introduced in [7] and the Hausdorff dimension HD(I(f)) of the set I(f) of all points escaping to infinity under forward iteration of f was estimated therein. In this paper we provide a closed formula for the exact value of HD(I(f)) identifying it with the critical exponent of the natural series introduced in [7]. This exponent is very easy to calculate for many concrete functions. In particular, we construct a function from this class which is of infinite order and for which HD(I(f)) = 0.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL