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Exact Hausdorff centered measure of symmetry Cantor sets

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  • Dai, Meifeng
  • Tian, Lixin

Abstract

Let K(λ1,λ2), the symmetry Cantor sets, be the attractor of an iterated function system {f1,f2,f3} on the line, where f1(x)=λ1x, f2(x)=λ2x+1-λ22,f3(x)=1-λ1+λ1x, x∈[0,1]. In this paper, we proved that if 1-2λ1-λ22⩾λ, where λ≡max{λ1,λ2}, then the exact Hausdorff centered measure Cs of K(λ1,λ2) equals 1, where s is the Hausdorff dimension of K(λ1,λ2).

Suggested Citation

  • Dai, Meifeng & Tian, Lixin, 2005. "Exact Hausdorff centered measure of symmetry Cantor sets," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 313-323.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:313-323
    DOI: 10.1016/j.chaos.2005.01.008
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    Cited by:

    1. Dai, Meifeng, 2006. "The equivalence of measures on Moran set in general metric space," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 55-64.
    2. Llorente, Marta & Morán, Manuel, 2012. "An algorithm for computing the centered Hausdorff measures of self-similar sets," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 246-255.
    3. Llorente, Marta & Eugenia Mera, M. & Morán, Manuel, 2017. "Rate of convergence: the packing and centered Hausdorff measures of totally disconnected self-similar sets," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 220-232.

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