Dimensions of non-differentiability points of Cantor functions

• Autorzy: Yuanyuan Yao , Yunxiu Zhang , Wenxia Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 195
• Numer: 2
• Strony: 113-125

Daty

wydano

2009

Twórcy

autor

Yuanyuan Yao

• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China

autor

Yunxiu Zhang

• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China

autor

Wenxia Li

• Department of Mathematics, East China Normal University, Shanghai 200241, P.R. China

Identyfikatory

DOI

10.4064/sm195-2-2