10 citations · 31 across the 14 of their papers we have counts for
15 papers · 1 filter
On hyperbolic dimension gap for entire functions
Volker Mayer, Mariusz Urbański
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 lat…
Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions
Volker Mayer, Mariusz Urbanski
This text provides an overview of the (geometric) thermodynamic formalism for transcendental meromorphic and entire functions with particular emphasis on geometric/fractal aspects…
The failure of Ruelle's property for entire functions
Volker Mayer, Anna Zdunik
We exhibit an analytic family of hyperbolic, even disjoint type, entire functions for which the hyperbolic dimension does not vary analytically. Additionally we answer several ques…
A lower bound of the hyperbolic dimension for meromorphic functions having a logarithmic Hölder tract
Volker Mayer
We improve existing lower bounds of the hyperbolic dimension for meromophic functions that have a logarithmic tract Ω which is a Hölder domain. These bounds are given in terms of t…
Thermodynamic formalism and integral means spectrum of asymptotic tracts for transcendental entire functions
Volker Mayer, Mariusz Urbański
We provide the full theory of thermodynamic formalism for a very general collection of entire functions in class . This class overlaps with the collection of all entire…
Real Analyticity for random dynamics of transcendental functions
Volker Mayer, Mariusz Urbanski, Anna Zdunik
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 o…