Kan Jiang

activity

20172022

λ

-Cantor sets

5 citations · 9 across the 7 of their papers we have counts for

collaborators

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15 papers · 1 filter

math.DS2022★ 1 cited

Thickness theorems with partial derivatives

Kan Jiang

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor…

math.DS2020

A nonlinear version of the Newhouse thickness theorem

Kan Jiang

Let $C_{1}$ and $C_{2}$ be two Cantor sets with convex hull $[0, 1]$ . Newhouse proved if $τ (C_{1}) \cdot τ (C_{2}) \geq 1$ , then the arithmetic sum $C_{1} + C_{2}$ is an interval, where $τ(C_i), 1\l…

math.DS2020★ 3 cited

On the sum of squares of middle-third Cantor set

Zhiqiang Wang, Kan Jiang, Wenxia Li +1

Let $C$ be the middle-third Cantor set. In this paper, we show that for every $x \in [0, 4]$ , there exist $x_{1}, x_{2}, x_{3}, x_{4} \in C$ such that $x = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2},$ which a…

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

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…

Thickness theorems with partial derivatives

A nonlinear version of the Newhouse thickness theorem

On the sum of squares of middle-third Cantor set

Multiplication on uniform λ-Cantor sets

Arithmetic on self-similar sets

Visibility of Cartesian products of Cantor sets

Multiplication on uniform $λ$ -Cantor sets