On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2004, v.11 no.1, pp.51-61

Baek, In-Soo (Departmen tof Mathematics, Pusan University of Foreign Studies)

Baek, In-Soo. (2004). ON A QUASI-SELF-SIMILAR MEASURE ON A SELF-SIMILAR SET ON THE WAY TO A PERTURBED CANTOR SET. 한국수학교육학회지시리즈B:순수및응용수학, 11(1), 51-61.

복사

Abstract

We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.

keywords: Hausdorff dimension, packing dimension, Cantor set, distribution set

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논문 상세

Vol.11 No.1

ON A QUASI-SELF-SIMILAR MEASURE ON A SELF-SIMILAR SET ON THE WAY TO A PERTURBED CANTOR SET

On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set

Abstract

한국수학교육학회지시리즈B:순수및응용수학