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<p>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.</p>

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Properties of a random Cantor set with overlaps

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Anna Chiara Lai,
  • Paola Loreti

摘要

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.