On the intersection of an m-part uniform Cantor set with its rational translation

Meifeng Dai and Lixin Tian

Chaos, Solitons & Fractals, 2008, vol. 38, issue 4, 962-969

Abstract: In this paper, we study an m-part uniform Cantor set with its rational translation. We give the fractal structure and the formula of the box-counting dimension of the intersection I(t). We find that the Hausdorff measures of these sets form a discrete spectrum whose non-zero values come only from translating the length t with its n-base expansion.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:38:y:2008:i:4:p:962-969

DOI: 10.1016/j.chaos.2007.01.030

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