TITLE:
Dimension of the Non-Differentiability Subset of the Cantor Function
AUTHORS:
Muquan Yan
KEYWORDS:
Hausdor Dimension, Packing Dimension, Cantor Ternary Function, Cantor Ternary Set
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.1,
January
8,
2020
ABSTRACT: The main purpose of this note is to estimate the size of the set Tμλ of points, at which the Cantor function is not differentiable and we find that the Hausdorff dimension of Tμλ is [log2/log3]2. Moreover, the Packing dimension of Tμλ is log2/log3. The log2 = loge2 is that if ax = N (a >0, and a≠1), then the number x is called the logarithm of N with a base, recorded as x = logaN, read as the logarithm of N with a base, where a is called logarithm Base number, N is called true number.