Lifeng Xi

activity

20122019

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

26 citations · 32 across the 5 of their papers we have counts for

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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.DS2018

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

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

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

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…

Multiplication on uniform λ-Cantor sets

Interiors of continuous images of the middle-third Cantor set

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

Lipschitz equivalence of self-similar sets with exact overlaps

Multiplication on self-similar sets with overlaps

Multiplication on uniform $λ$ -Cantor sets