62 citations · 139 across the 24 of their papers we have counts for
25 papers
Local Scaling and Dimension Distortion of Generalized Cantor Functions
Yuanzhe Shi, Zhantu Yang, Jun Jason Luo
Let \(μ\) be a self-similar Cantor measure on \(\mathbb R\) associated with a probability weight vector \(\mathbf p\), let \(K=\operatorname{supp}μ\), and let \(F\) denote the dist…
To Define the Core Entropy for All Polynomials Having a Connected Julia Set
Jun Luo, Bo Tan, Yi Yang +1
For all polynomials with that have a connected filled Julia set , we introduce a new quantity , such that $h_{\rm GCE}\left(f^n\right)=n\c…
A model for planar compacta and rational Julia sets
Jun Luo, Yi Yang, Xiaoting Yao
A Peano compactum is a compact metric space having locally connected components such that at most finitely many of them are of diameter greater than any fixed number C>0. Given a c…
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…
On continuous extension of conformal homeomorphisms of infinitely connected planar domains
Jun Luo, Xiao-Ting Yao
We consider conformal homeomorphisms of generalized Jordan domains onto planar domains %, possibly {\bf infinitely connected}, that satisfy both of the next two conditi…
On Lambda Function and a Quantification of Torhorst Theorem
Li Feng, Jun Luo, Xiao-Ting Yao
To any compact we associate a map -- the lambda function of -- such that a planar continuu…
Ricci-flat graphs with girth four
Weihua He, Jun Luo, Chao Yang +1
Lin-Lu-Yau introduced an interesting notion of Ricci curvature for graphs and obtained a complete characterization for all Ricci-flat graphs with girth at least five [1]. In this p…
Peano Model for Planar Compacta and a Lemma by Beardon
Jun Luo, Yi Yang, Xiao-Ting Yao
It is known that, among all the monotone decompositions of a planar compact set K with Peano hyperspaces, there exists a unique one that is finer than all the others. We call it th…
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…
A Core Decomposition of Compact Sets in the Plane
Benoit Loridant, Jun Luo, Yi Yang
A Peano continuum means a locally connected continuum. A compact metric space is called a \emph{Peano compactum} if all its components are Peano continua and if for any constant $C…
On the Lipschitz equivalence of self-affine sets
Jun Jason Luo
Let be an expanding matrix with integer entries and be a finite digit set. Then the pair defines a unique in…
Fibers and local connectedness of planar continua
Benoît Loridant, Jun Luo
We describe non-locally connected planar continua via the concepts of fiber and numerical scale. Given a continuum and , we show that the set o…
Lipschitz equivalence of Cantor sets and irreducibility of polynomials
Jun Jason Luo, Huo-Jun Ruan, Yi-Ling Wang
In the paper, we provide an effective method for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of polynomials. We…
Topological properties of self-similar fractals with one parameter
Jun Jason Luo, Lian Wang
In this paper, we study two classes of planar self-similar fractals with a shifting parameter . The first one is a class of self-similar tiles by shift…
Self-similar sets, simple augmented trees, and their Lipschitz equivalence
Jun Jason Luo
Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the paper, we introduce a not…
On cut sets of attractors of iterated function systems
Benoît Loridant, Jun Luo, Tarek Sellami +1
In this paper, we study cut sets of attractors of iteration function systems (IFS) in . Under natural conditions, we show that all irreducible cut sets of these attra…
A numerical scale for non locally connected planar continua
Timo Jolivet, Benoît Loridant, Jun Luo
We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a contin…
Lipschitz equivalence of self-similar sets and hyperbolic boundaries II
Guo-Tai Deng, Ka-Sing Lau, Jun Jason Luo
In \cite{LuLa13}, two of the authors initiated a study of Lipschitz equivalence of self-similar sets through the augmented trees, a class of hyperbolic graphs introduced by Kaimano…
Rauzy fractals with countable fundamental group
Timo Jolivet, Benoît Loridant, Jun Luo
We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. Thi…
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…
Moran Sets and Hyperbolic Boundaries
Jun Jason Luo
In the paper, we prove that a Moran set is homeomorphic to the hyperbolic boundary of the representing symbolic space in the sense of Gromov, which generalizes the results of Lau a…
Boundaries of Disk-like Self-affine Tiles
King-Shun Leung, Jun Jason Luo
Let be a disk-like self-affine tile generated by an integral expanding matrix and a consecutive collinear digit set , and let $f(x)=x^{2}…
Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
King-Shun Leung, Jun Jason Luo
In the paper, we focus on the connectedness of planar self-affine sets generated by an integer expanding matrix with and a collinear digit s…
Lipschitz equivalence of self-similar sets and hyperbolic boundaries
Jun Jason Luo, Ka-Sing Lau
In [9] Kaimanovich introduced the concept of augmented tree on the symbolic space of a self-similar set. It is hyperbolic in the sense of Gromov, and it was shown in [13] that unde…