Mariusz Urba'nski

collaborators

3 papers

math.DS2026

Asymptotics of the Hausdorff measure for the Gauss map and its linearized analogue

RafaÅ Tryniecki, Mariusz UrbaÅski, Anna Zdunik

Let $G (x) := {1/ x}$ be the Gauss map. By $g_{n} (x) = \frac{1}{x + n}$ we denote its continuous/real analytic inverse branches. We define iterated function system (IFS) $G_{n}$ by limiting…

math.DS2025

Rigorous Hausdorff dimension estimates for conformal fractals

Vasileios Chousionis, Dmitriy Leykekhman, Mariusz UrbaÅski +1

We develop a versatile framework which allows us to rigorously estimate the Hausdorff dimension of maximal conformal graph directed Markov systems in $R^{n}$ for $n \geq 2$ .…

math.DS2025

The dimension spectrum of the infinitely generated Apollonian gasket

Vasileios Chousionis, Dmitriy Leykekhman, Mariusz UrbaÅski +1

We prove that the infinitely generated Apollonian gasket has full Hausdorff dimension spectrum. Our proof, which is computer assisted, relies on an iterative technique introduced b…