Work

The dimension spectrum of the infinitely generated Apollonian gasket

Year: 2026

Type: article

Abstract: 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 by the first three authors [Chousionis, Leykekhman, and Urbański. The dimension spectrum of conformal graph directed Markov systems. Selecta Math. (N.S.) 25 (2019), 74] and on a flexible method for rigorously estimating Hausdorff dimensions of limit sets of conformal iterated function systems, which we recently developed [Chousionis et al . Rigorous Hausdorff dimension estimates for conformal fractals. Preprint , 2024, arXiv:2408.06330]. Another key ingredient in our proof is obtaining, for the first time, reasonably sized distortion constants for the (infinite) Apollonian iterated function system.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2026.10307

Authors: VASILIS CHOUSIONIS, DMITRIY LEYKEKHMAN, MARIUSZ URBANSKI, ERIK WENDT

Institutions: University of Connecticut, University of North Texas

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Awards: G1634019874, Rigorous Hausdorff dimension estimates for conformal fractals, Some topics in Analysis and Probability in Metric Measure Spaces, Random Matrices, and Diffusions