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

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  • Dai, Meifeng
  • Tian, Lixin

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.

Suggested Citation

  • Dai, Meifeng & Tian, Lixin, 2008. "On the intersection of an m-part uniform Cantor set with its rational translation," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 962-969.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:962-969
    DOI: 10.1016/j.chaos.2007.01.030
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    2. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    3. Dai, Meifeng & Tian, Lixin, 2007. "Some properties for the intersection of Moran sets with their translates," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 757-764.
    4. Dai, Meifeng & Tian, Lixin, 2007. "Intersection of the Sierpinski carpet with its rational translate," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 179-187.
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