REAL ANALYTICITY FOR RANDOM DYNAMICS OF TRANSCENDENTAL FUNCTIONS

Mayer, Volker; Urbański, Mariusz; Zdunik, Anna

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1017/etds.2018.42

Title :

REAL ANALYTICITY FOR RANDOM DYNAMICS OF TRANSCENDENTAL FUNCTIONS

Author(s) :

Mayer, Volker [Auteur]

Université de Lille
Urbański, Mariusz [Auteur]
Zdunik, Anna [Auteur]

Journal title :

Ergodic Theory and Dynamical Systems

Pages :

490-520

Publisher :

Cambridge University Press (CUP)

Publication date :

2017-02-17

ISSN :

0143-3857

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh [15] leading to a simple ...
Show more >Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement of work by Rugh [15] leading to a simple approach to analyticity. We work under very mild dynamical assumptions. Just the iterates of the Perron-Frobenius operator are assumed to converge. We also provide Bowen's formula expressing the almost sure Hausdorff dimension of the radial fiberwise Julia sets in terms of the zero of an expected pressure function. Our main application establishes real analyticity for the variation of this dimension for suitable hyperbolic random systems of entire or meromorphic functions.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :