Stable intersections of regular Cantor sets with large Hausdorff dimensions

• 成果类型: Article
• 署名作者: Moreira, CGTD; Yoccoz, JC
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2001
• 页码: 45-96
• 关键词: arithmetic sum; difference

摘要

In this paper we prove a conjecture by J. Palis according to which the arithmetic difference of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one then, in almost all cases, there are translations of them whose intersection persistently has Hausdorff dimension.