Commun. Korean Math. Soc. 2005; 20(4): 695-702
Printed December 1, 2005
Copyright © The Korean Mathematical Society.
In-Soo Baek
Pusan University of Foreign Studies
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.
Keywords: Hausdorff dimension, packing dimension, Cantor set, self-similar measure, distribution set
MSC numbers: 28A78
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