Properties of a random Cantor set with overlaps
Anna Chiara Lai, Paola Loreti
TL;DR
This paper investigates the topological and dimensional properties of a random Cantor set with overlaps, generated by an IFS with the Golden Mean, extending known results to cases where the Open Set Condition does not hold.
Contribution
It introduces a novel analysis of a random Cantor set with overlaps using non-integer base expansions, extending existing formulas beyond the Open Set Condition.
Findings
Determines the Hausdorff dimension of the set.
Analyzes the topological structure of the set.
Extends formulas to overlapping cases.
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Computability, Logic, AI Algorithms · Topological and Geometric Data Analysis