Hausdorff dimension of the Apollonian gasket

• 成果类型: Article
• 署名作者: Vytnova, Polina L.; Wormell, Caroline L.
• 署名单位: University of Surrey; University of Sydney
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01311-y
• 发表日期: 2025
• 页码: 909-946
• 关键词: packing

摘要

The Apollonian gasket is a well-studied circle packing. Important properties of the packing, including the distribution of the circle radii, are governed by its Hausdorff dimension. No closed form is currently known for the Hausdorff dimension, and its computation is a special case of a more general and hard problem: effective, rigorous estimates of dimension of a parabolic limit set. In this paper we develop an efficient method for solving this problem which allows us to compute the dimension of the gasket to 128 decimal places and rigorously justify the error bounds. We expect our approach to generalise easily to other parabolic fractals.