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 2018 · math.DSShow all

5 papers · 2 filters

math.DS2018★ 2 cited

Critical base for the unique codings of fat Sierpinski gasket

Derong Kong, Wenxia Li

Given $β \in (1, 2)$ the fat Sierpinski gasket $S_{β}$ is the self-similar set in $R^{2}$ generated by the iterated function system (IFS) \[ f_{β,d}(x)=\frac{x+d}β,\quad…

math.DS2018

On the structure of $λ$ -Cantor set with overlaps

Karma Dajani, Derong Kong, Yuanyuan Yao

Given $λ \in (0, 1)$ , let $E_{λ}$ be the self-similar set generated by the iterated function system ${x /3, (x + λ) /3, (x + 2) /3}$ . Then $E_{λ}$ is a self-similar set with overlaps. We obtain…

math.DS2018★ 9 cited

Relative bifurcation sets and the local dimension of univoque bases

Pieter Allaart, Derong Kong

Fix an alphabet $A = {0, 1, \dots, M}$ with $M \in N$ . The univoque set $U$ of bases $q \in (1, M + 1)$ in which the number $1$ has a unique expansion over the alphabet $A…

math.DS2018★ 17 cited

On the continuity of the Hausdorff dimension of the univoque set

Pieter Allaart, Derong Kong

In a recent paper [Adv. Math. 305:165--196, 2017], Komornik et al.~proved a long-conjectured formula for the Hausdorff dimension of the set $U_{q}$ of numbers having a uniq…

math.DS2018

The $β$ -transformation with a hole at 0

Charlene Kalle, Derong Kong, Niels Langeveld +1

For $β \in (1, 2]$ the $β$ -transformation $T_{β} : [0, 1) \to [0, 1)$ is defined by $T_{β} (x) = β x (mod 1)$ . For $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set of $T_{β}$ with hole $(0, t)$ giv…

Critical base for the unique codings of fat Sierpinski gasket

On the structure of λ-Cantor set with overlaps

Relative bifurcation sets and the local dimension of univoque bases

On the continuity of the Hausdorff dimension of the univoque set

The β-transformation with a hole at 0

On the structure of $λ$ -Cantor set with overlaps

The $β$ -transformation with a hole at 0