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http://dx.doi.org/10.4134/BKMS.2004.41.1.013

CANTOR DIMENSION AND ITS APPLICATION  

Baek, In-Soo (Department of Matematics, Pusan University of Foreign Studies)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 13-18 More about this Journal
Abstract
We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.
Keywords
weak local dimension; deranged Cantor set; Hausdorff dimension; packing dimension;
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  • Reference
1 Dimensions of weakly convergent deranged Cantor sets /
[] / Real Anal. Exchange
2 Week local dimension on deranged Cantor set /
[] / Real Analysis Exchange
3 /
[] / Techniques in fractal geometry
4 Hausdorff dimension of perturbed Cantor sets without some boundedness condition /
[] / Acta Math. Hungar   DOI
5 Dimensions of the perturbed Cantor set /
[ I.S.Baek ] / Real Analysis Exchange
6 /
[ K.J.Falconer ] / Fractal geometry
7 Two definitions of fractional dimension /
[ C.Tricot ] / Math. Proc. Cambridge Philos. Soc.   DOI