28 citations · 59 across the 20 of their papers we have counts for
20 papers
Connected p.c.f self-similar fractals satisfying the angle separation condition have conformal dimension 1
Hui Rao, Zhi-Ying Wen, Qihan Yuan +1
Let be a graph-directed iterated function system (GIFS) satisfying the finite post-critical points property (p.c.f), and assume that the attractors $(M_\ell)_{\ell\i…
Box-counting measure of metric spaces
Liang-yi Huang, Hui Rao, Zhiying Wen +1
In this paper, we introduce a new notion called the \emph{box-counting measure} of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a…
A dimension drop phenomenon of fractal cubes
Liangyi Huang, Hui Rao
Let E be a metric space. We introduce a notion of connectedness index of E, which is the Hausdor? dimension of the union of non-trivial connected components of E. We show that the…
Ergodicity for -adic continued fraction algorithms
Hui Rao, Shin-ichi Yasutomi
Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of -adic multidimensional continued fraction algorithms,…
Characterization of complementing pairs of
Hui Rao, Ya-min Yang, Yuan Zhang
Let be subsets of an abelian group . A pair is called a -pair if and is the direct sum of and . The -pairs are ch…
Invariance of multifractal spectrum of uniform self-affine measures and its applications
Hui Rao, Ya-min Yang, Yuan Zhang
We study the bi-Lipschitz classification of Bedford-McMullen carpets which are totally disconnected. Let be a such carpet and let be the uniform Bernoulli measure on .…
Dissecting a square into congruent polygons
Hui Rao, Lei Ren, Yang Wang
We study the dissection of a square into congruent convex polygons. Yuan \emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298]…
Space-filling curves of self-similar sets (III): Skeletons
Hui Rao, Shu-Qin Zhang
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Ed…
Every component of a fractal square is a Peano continuum
Jun Luo, Hui Rao, Ying Xiong
This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or…
Lipschitz invariance of walk dimension on connected self-similar sets
Hui Rao, Qingsong Gu
Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is…
Lipschitz equivalence of fractals and finite state automaton
Hui Rao, Yunjie Zhu
The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using…
Space-filling curves of self-similar sets (I): Iterated function systems with order structure
Hui Rao, Shu-Qin Zhang
This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, w…
Higher dimensional Frobenius problem: Maximal saturated cone, growth function and rigidity
Ai-hua Fan, Hui Rao, Yuan Zhang
We consider integral vectors located in a half-space of () and study the structure of the additive semi-group $X_1 \…
Higher dimensional Frobenius problem and Lipschitz equivalence of Cantor sets
Hui Rao, Yuan Zhang
The higher dimensional Frobenius problem was introduced by a preceding paper [Fan, Rao and Zhang, Higher dimensional Frobenius problem: maximal saturated cones, growth function and…
Affine embeddings and intersections of Cantor sets
De-Jun Feng, Wen Huang, Hui Rao
Let be two self-similar sets. Under mild conditions, we show that can be -embedded into if and only if it can be affinely embedded into ; further…
Self-similar subsets of the Cantor set
De-Jun Feng, Hui Rao, Yang Wang
In this paper, we study the following question raised by Mattila in 1998: what are the self-similar subsets of the middle-third Cantor set $\C$? We give criteria for a complete cla…
Classification of tile digit sets as product-forms
Chun-Kit Lai, Ka-Sing Lau, Hui Rao
Let be an expanding matrix on with integral entries. A fundamental question in the fractal tiling theory is to understand the structure of the digit set ${\mathcal…
Lipschitz Equivalence of Self-Similar Sets: Algebraic and Geometric Properties
Hui Rao, Huo-Jun Ruan, Yang Wang
In this paper we provide an up-to-date survey on the study of Lipschitz equivalence of self-similar sets. Lipschitz equivalence is an important property in fractal geometry because…
Topological Structure of Fractal Squares
Ka-Sing Lau, Jun Jason Luo, Hui Rao
Given an integer and a digit set , there is a self-similar set satisfying the set equation: $F=(F+{\mathcal…
Spectral structure of digit sets of self-similar tiles on
Chun-Kit Lai, Ka-Sing Lau, Hui Rao
We study the structure of the digit sets for the integral self-similar tiles (we call such a {\it tile digit set} with respect to…