On the Lebesgue measure of the Feigenbaum Julia set

• 成果类型: Article
• 署名作者: Dudko, Artem; Sutherland, Scott
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00949-8
• 发表日期: 2020
• 页码: 167-202
• 关键词: hausdorff dimension; UNIVERSALITY; POLYNOMIALS; DYNAMICS

摘要

We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than 2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.