7 citations · 10 across the 6 of their papers we have counts for
7 papers
Coding multiplicity in self-similar sets on the line
Károly Simon, Jian-Ci Xiao
We study coding multiplicity for self-similar sets on the real line. When the similarity dimension exceeds one, almost every point with respect to the natural self-similar measure…
From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
Huo-Jun Ruan, Jian-Ci Xiao
Let be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from to a…
The connectedness of Sierpiński sponges with rotational and reflectional components and associated graph-directed systems
Huo-Jun Ruan, Jian-Ci Xiao
We provide two methods to characterize the connectedness of all -dimensional generalized Sierpiński sponges whose corresponding IFSs are allowed to have rotational and reflectio…
On the existence of cut points of connected generalized Sierpinski carpets
Huo-Jun Ruan, Yang Wang, Jian-Ci Xiao
In a previous work joint with Dai and Luo, we show that a connected generalized Sierpiński carpet (or shortly a GSC) has cut points if and only if the associated -th Hata graph…
Connectedness and local cut points of generalized Sierpinski carpets
Xin-Rong Dai, Jun Luo, Huo-Jun Ruan +2
We investigate a homeomorphism problem on a class of self-similar sets called generalized Sierpinski carpets (or shortly GSCs). It follows from two well-known results by Hata and W…
Fractal squares with finitely many connected components
Jian-Ci Xiao
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish…
A note on the proofs of generalized radon inequality
Yongtao Li, Xian-Ming Gu, Jianci Xiao
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find math…