Title :

THERMODYNAMIC FORMALISM AND INTEGRAL MEANS SPECTRUM OF LOGARITHMIC TRACTS FOR TRANSCENDENTAL ENTIRE FUNCTIONS

Author(s) :

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

Journal title :

Transactions of the American Mathematical Society

Pages :

7669-7711

Publisher :

American Mathematical Society

Publication date :

2019-10-21

ISSN :

0002-9947

English keyword(s) :

May 25 2022. 2010 Mathematics Subject Classification. Primary 30D05 37D35
Secondary 37F10 37F45 28A80
May 25
2022. 2010 Mathematics Subject Classification. Primary 30D05
37D35
Secondary 37F10
37F45
28A80

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We provide an entirely new approach to the theory of thermodynamic formalism for entire functions of bounded type. The key point is that we introduce an integral means spectrum for logarithmic tracts which takes care of ...
Show more >We provide an entirely new approach to the theory of thermodynamic formalism for entire functions of bounded type. The key point is that we introduce an integral means spectrum for logarithmic tracts which takes care of the fractal behavior of the boundary of the tract near infinity. It turns out that this spectrum behaves well as soon as the tracts have some sufficiently nice geometry which, for example, is the case for quasidisk, John or Hölder tracts. In these cases we get a good control of the corresponding transfer operators, leading to full thermodynamic formalism along with its applications such as exponential decay of correlations, central limit theorem and a Bowen's formula for the Hausdorff dimension of radial Julia sets. This approach covers all entire functions for which thermodynamic formalism has been so far established and goes far beyond. It applies in particular to every hyperbolic function from any Eremenko-Lyubich analytic family of Speiser class S provided this family contains at least one function with Hölder tracts. The latter is, for example, the case if the family contains a Poincaré linearizer.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL