[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2005.20.4.695

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

BAEK, IN-Soo (Department of Mathematics Pusan University of Foreign Studies)

Publication Information

Communications of the Korean Mathematical Society / v.20, no.4, 2005 , pp. 695-702 More about this Journal

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;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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