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.
Properties of a random Cantor set with overlaps / Lai, A.C., Loreti, P.. - In: RESEARCH IN NUMBER THEORY. - ISSN 2363-9555. - 12:3(2026). [10.1007/s40993-026-00761-y]
Properties of a random Cantor set with overlaps
Anna Chiara Lai
;Paola Loreti
2026
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.File allegati a questo prodotto
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