Dimensions of non-differentiability points of Cantor functions

Yuanyuan Yao, Yunxiu Zhang, and Wenxia Li. "Dimensions of non-differentiability points of Cantor functions." Studia Mathematica 195.2 (2009): 113-125. <http://eudml.org/doc/284919>.

@article{YuanyuanYao2009,
abstract = {For a probability vector (p₀,p₁) there exists a corresponding self-similar Borel probability measure μ supported on the Cantor set C (with the strong separation property) in ℝ generated by a contractive similitude $h_\{i\}(x) = a_\{i\}x + b_\{i\}$, i = 0,1. Let S denote the set of points of C at which the probability distribution function F(x) of μ has no derivative, finite or infinite. The Hausdorff and packing dimensions of S have been found by several authors for the case that $p_\{i\} > a_\{i\}$, i = 0,1. However, when p₀ < a₀ (or equivalently p₁ < a₁) the structure of S changes significantly and the previous approaches fail to be effective any more. The present paper is devoted to determining the Hausdorff and packing dimensions of S for the case p₀ < a₀.},
author = {Yuanyuan Yao, Yunxiu Zhang, Wenxia Li},
journal = {Studia Mathematica},
keywords = {Hausdorff and packing dimensions; non-differentiability points; Cantor functions},
language = {eng},
number = {2},
pages = {113-125},
title = {Dimensions of non-differentiability points of Cantor functions},
url = {http://eudml.org/doc/284919},
volume = {195},
year = {2009},
}

TY - JOUR
AU - Yuanyuan Yao
AU - Yunxiu Zhang
AU - Wenxia Li
TI - Dimensions of non-differentiability points of Cantor functions
JO - Studia Mathematica
PY - 2009
VL - 195
IS - 2
SP - 113
EP - 125
AB - For a probability vector (p₀,p₁) there exists a corresponding self-similar Borel probability measure μ supported on the Cantor set C (with the strong separation property) in ℝ generated by a contractive similitude $h_{i}(x) = a_{i}x + b_{i}$, i = 0,1. Let S denote the set of points of C at which the probability distribution function F(x) of μ has no derivative, finite or infinite. The Hausdorff and packing dimensions of S have been found by several authors for the case that $p_{i} > a_{i}$, i = 0,1. However, when p₀ < a₀ (or equivalently p₁ < a₁) the structure of S changes significantly and the previous approaches fail to be effective any more. The present paper is devoted to determining the Hausdorff and packing dimensions of S for the case p₀ < a₀.
LA - eng
KW - Hausdorff and packing dimensions; non-differentiability points; Cantor functions
UR - http://eudml.org/doc/284919
ER -