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Simple approach to multifractal spectrum of a self-similar Cantor set

백인수
대한수학회 (The Korean Mathematical Society)|2005.10|대한수학회논문집 (Communications of the KMS)|제20권 제4호|pp. 695-702

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참고문헌

주제분류수학

초록

Abstract

We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Cantor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self-similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter determines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

참고문헌 (18)

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관련 논문AI추천

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