Title :

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

Author(s) :

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

Journal title :

Geometric And Functional Analysis

Pages :

53-80

Publisher :

Springer Verlag

Publication date :

2022-01-25

ISSN :

1016-443X

HAL domain(s) :

Mathématiques [math]

English abstract : [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] ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL