Kan Jiang

activity

20142022

most citedMultiple expansions of real numbers with digits set

{0, 1, q}

7 citations · 55 across the 25 of their papers we have counts for

collaborators

Showing 2019Show all

5 papers · 1 filter

math.DS2019★ 5 cited

Multiplication on uniform $λ$ -Cantor sets

Jiangwen Gu, Kan Jiang, Lifeng Xi +1

Let $C$ be the middle-third Cantor set. Define $C * C = {x * y : x, y \in C}$ , where $* = +, -, \cdot, \div$ (when $* = \div$ , we assume $y \neq = 0$ ). Steinhaus \cite{HS} proved in 1917 that \[ C-C=[-1,1]…

math.DS2019

Arithmetic on self-similar sets

Bing Zhao, Xiaomin Ren, Jiali Zhu +1

Let $K_{1}$ and $K_{2}$ be two one-dimensional homogeneous self-similar sets. Let $f$ be a continuous function defined on an open set $U \subset R^{2}$ . Denote the continuous i…

math.DS2019★ 3 cited

Visibility of Cartesian products of Cantor sets

Tingyu Zhang, Kan Jiang, Wenxia Li

Let $K_{λ}$ be the attractor of the following IFS \begin{equation*} \{f_1(x)=λx, f_2(x)=λx+1-λ\}, \;\;0<λ<1/2. \end{equation*} Given $α \geq 0$ , we say the line $y = α x$ is visible thro…

math.DS2019★ 3 cited

Arithmetic on Moran sets

Xiaomin Ren, Li Tian, Jiali Zhu +1

Let $(M, c_{k}, n_{k})$ be a class of Moran sets. We assume that the convex hull of any $E \in (M, c_{k}, n_{k})$ is $[0, 1]$ . Let $A, B$ be two non-empty sets in $\mathbb{R…

math.NT2019

On arithmetic progressions in self-similar sets

Kan Jiang, Qiyang Pei, Lifeng Xi

Given a sequence ${b_{i}}_{i = 1}^{n}$ and a ratio $λ \in (0, 1),$ let $E = \cup_{i = 1}^{n} (λ E + b_{i})$ be a homogeneous self-similar set. In this paper, we study the existence and maximal l…

Multiplication on uniform λ-Cantor sets

Arithmetic on self-similar sets

Visibility of Cartesian products of Cantor sets

Arithmetic on Moran sets

On arithmetic progressions in self-similar sets

Multiplication on uniform $λ$ -Cantor sets