3 papers
math.DS2025
The dimension spectrum of the infinitely generated Apollonian gasket
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański +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…
math.DS2025
Asymptotics of the Hausdorff measure for the Gauss map and its linearized analogue
Rafał Tryniecki, Mariusz Urbański, Anna Zdunik
Let be the Gauss map. By we denote its continuous/real analytic inverse branches. We define iterated function system (IFS) by limiting…
math.DS2024
Rigorous Hausdorff dimension estimates for conformal fractals
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański +1
We develop a versatile framework which allows us to rigorously estimate the Hausdorff dimension of maximal conformal graph directed Markov systems in for .…