2004•Bulletin of the Korean Mathematical SocietyRequires access

CANTOR DIMENSION AND ITS APPLICATION

In-Soo Baek

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.

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Key concepts: Cantor set, Mathematics, Cantor function, Packing dimension, Cantor's diagonal argument, Hausdorff dimension, Effective dimension, Minkowski–Bouligand dimension