Kan Jiang

activity

20142020

λ

-Cantor sets

5 citations · 8 across the 6 of their papers we have counts for

collaborators

6 papers

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.MG2020

On continuous images of self-similar sets

Yuanyuan Li, Jiaqi Fan, Jiangwen Gu +2

Let $(M, c_{k}, n_{k}, κ)$ be a class of homogeneous Moran sets. Suppose $f (x, y) \in C^{3}$ is a function defined on $R^{2}$ . Given $E_{1}, E_{2} \in (M, c_{k}, n_{k}, κ)$ …

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.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…

math.DS2014

On univoque points for self-similar sets

Simon Baker, Karma Dajani, Kan Jiang

Let $K \subseteq R$ be the unique attractor of an iterated function system. We consider the case where $K$ is an interval and study those elements of $K$ with a unique codin…