INTERSECTING RANDOM TRANSLATES OF INVARIANT CANTOR SETS

• 成果类型: Article
• 署名作者: KENYON, R; PERES, Y
• 署名单位: Hebrew University of Jerusalem
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01245092
• 发表日期: 1991
• 页码: 601-629
• 关键词: sofic systems

摘要

Given two Cantor sets X and Y in [0, 1), invariant under the map x bar-arrow-pointing-right b x mod 1, the Hausdorff dimension of (X + t) intersection Y is constant almost everywhere. When X, Y are defined by admissible digits in base b, and more generally by sofic systems, we compute this dimension in terms of the largest Lyapunov exponent of a random product of matrices. The results are extended to higher dimensions and multiple intersections.