SIMPLE APPROACH TO MULTIFRACTAL SPECTRUM OF A SELF-SIMILAR CANTOR SET

Title & Authors
SIMPLE APPROACH TO MULTIFRACTAL SPECTRUM OF A SELF-SIMILAR CANTOR SET
BAEK, IN-Soo;

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 self­similar 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.
Keywords
Hausdorff dimension;packing dimension;Cantor set;self-similar measure;distribution set;
Language
English
Cited by
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