Properties of a random Cantor set with overlaps

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Anna Chiara Lai, Paola Loreti
Cited by: 0

Abstract

We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set Condition fails. Our methodology is based on the theory of expansions in non-integer bases.

Fields of Study & Subjects

Mathematical Dynamics and Fractals advanced mathematical theories Advanced Mathematical Theories and Applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
28 January 2026
Document type
Preprint