Lifeng Xi

activity

20122019

most citedLipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem

26 citations · 57 across the 16 of their papers we have counts for

collaborators

16 papers

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.MG2019

On the Separation Structure of Lalley-Gatzouras Fractals

Li-Feng Xi, Jun Jie Miao, Ying Xiong

We obtain a necessary and sufficient condition for Lalley-Gatzouras sets to be uniform disconnected. This enable us to find all Lalley-Gatzouras sets which are quasisymmetrically e…

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.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…