On Intersections of Cantor Sets: Hausdorff Measure
Steen Pedersen, Jason D. Phillips
TL;DR
This paper derives formulas to estimate the Hausdorff measure and dimension of intersections of specific Cantor sets with their translates, advancing understanding of fractal geometry intersections.
Contribution
It provides new formulas for bounds on Hausdorff measure and exact Hausdorff dimensions of Cantor set intersections with their translations.
Findings
Formulas for bounds on Hausdorff measure of Cantor set intersections
Explicit formula for Hausdorff dimensions of these intersections
Enhanced understanding of fractal set intersections
Abstract
We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Functional Equations Stability Results