4 papers · 1 filter
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…
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 .…
On the dimension spectrum of infinite subsystems of continued fractions
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if is any arithmetic pro…
The dimension spectrum of graph directed Markov systems
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of general conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We perform a comprehe…