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 2018Show all

6 papers · 1 filter

math.DS2018

Multiple representations of real numbers on self-similar sets with overlaps

Xiaomin Ren, Jiali Zhu, Li Tian +1

Let $K$ be the attractor of the following IFS ${f_{1} (x) = λ x, f_{2} (x) = λ x + c - λ, f_{3} (x) = λ x + 1 - λ},$ where $f_{1} (I) \cap f_{2} (I) \neq = \emptyset, (f_{1} (I) \cup f_{2} (I)) \cap f_{3} (I) = \emptyset,$ …

math.DS2018★ 6 cited

Interiors of continuous images of the middle-third Cantor set

Kan Jiang, Lifeng Xi

Let $C$ be the middle-third Cantor set, and $f$ a continuous function defined on an open set $U \subset R^{2}$ . Denote the image \begin{equation*} f_{U}(C,C)=\{f(x,y):(x,y)…

math.DS2018★ 2 cited

Arithmetic representations of real numbers in terms of self-similar sets

Kan Jiang, Lifeng Xi

Suppose $n \geq 2$ and $A_{i} \subset {0, 1, \dots, (n - 1)}$ for $i = 1, \dots, l,$ let $K_{i} = ⋃_{a \in A_{i}} n^{- 1} (K_{i} + a)$ be self-similar sets c…

math.DS2018★ 6 cited

Lipschitz equivalence of self-similar sets with exact overlaps

Kan Jiang, Songjing Wang, Lifeng Xi

In this paper, we study a class $A (λ, n, m)$ of self-similar sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $λ$ . We obtain a necessary conditi…

math.DS2018★ 2 cited

Multiplication on self-similar sets with overlaps

Li Tian, Jiangwen Gu, Qianqian Ye +2

Let $A, B \subset R$ . Define $A \cdot B = {x \cdot y : x \in A, y \in B} .$ In this paper, we consider the following class of self-similar sets with overlaps. Let $K$ be the attra…

math.DS2018★ 4 cited

Projections of cartesian products of the self-similar sets without the irrationality assumption

Kan Jiang

Let $β > 1$ . Define a class of similitudes \[S=\left\{f_{i}(x)=\dfrac{x}{β^{n_i}}+a_i:n_i\in \mathbb{N}^{+}, a_i\in \mathbb{R}\right\}.\] Let $A$ be the collection of all t…