4 papers
Inner Functions, Composition Operators, Symbolic Dynamics and Thermodynamic Formalism
Oleg Ivrii, Mariusz Urbański
In this paper, we use thermodynamic formalism to study the dynamics of inner functions acting on the unit disk. If the Denjoy-Wolff point of is in the open unit disk, then…
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…
Estimating Hausdorff measure for Denjoy maps
Łukasz Pawelec, Mariusz Urbański
By employing the recurrence method worked out in `Estimating the Hausdorff measure by recurrence', we provide effective lower estimates of the proper--dimensional Hausdorff measure…
Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions
Christopher J. Bishop, Kirill Lazebnik, Mariusz Urbański
We show that any dynamics on any planar set discrete in some domain can be realized by the postcritical dynamics of a function holomorphic in , up to a small perturbatio…