D. Kong

activity

20112022

most citedHausdorff dimension of unique beta expansions

46 citations · 180 across the 37 of their papers we have counts for

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Showing 2022Show all

4 papers · 1 filter

math.DS2022

Projections of four corner Cantor set: total self-similarity, spectrum and unique codings

Derong Kong, Beibei Sun

Given $ρ \in (0, 1/4]$ , the four corner Cantor set $E \subset R^{2}$ is a self-similar set generated by the iterated function system \[ \left\{(ρx, ρy), \quad(ρx, ρy+1-ρ),\qu…

math.DS2022

Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals

Yu Hu, Yan Huang, Derong Kong

Given a positive integer $M$ and a real number $x \in (0, 1]$ , we call $q \in (1, M + 1]$ a univoque simply normal base of $x$ if there exists a unique simply normal sequence $(d_i)\in\{0,…

math.NT2022★ 4 cited

Rational Points in Translations of The Cantor Set

Kan Jiang, Derong Kong, Wenxia Li +1

Given two coprime integers $p \geq 2$ and $q \geq 3$ , let $D_{p} \subset [0, 1)$ consist of all rational numbers which have a finite $p$ -ary expansion, and let $$ K(q, \mathcal{A})=\bigg\{…

math.DS2022

Intersections of middle- $α$ Cantor sets with a fixed translation

Yan Huang, Derong Kong

For $λ \in (0, 1/3]$ let $C_{λ}$ be the middle- $(1 - 2 λ)$ Cantor set in $R$ . Given $t \in [- 1, 1]$ , excluding the trivial case we show that \[ Λ(t):=\left\{λ\in(0,1/3]: C_λ\cap(C_λ+t…

Projections of four corner Cantor set: total self-similarity, spectrum and unique codings

Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals

Rational Points in Translations of The Cantor Set

Intersections of middle-α Cantor sets with a fixed translation

Intersections of middle- $α$ Cantor sets with a fixed translation