S. Baker

activity

20122023

most citedUnique expansions and intersections of Cantor sets

10 citations · 77 across the 32 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.DS2017

Exceptional digit frequencies and expansions in non-integer bases

Simon Baker

In this paper we study the set of digit frequencies that are realised by elements of the set of $β$ -expansions. The main result of this paper demonstrates that as $β$ approaches $1…

math.DS2017

Numbers with simply normal $β$ -expansions

Simon Baker, Derong Kong

In [Bak] the first author proved that for any $β \in (1, β_{K L})$ every $x \in (0, \frac{1}{β - 1})$ has a simply normal $β$ -expansion, where $β_{K L} \approx 1.78723$ is the Komornik-Loret…

math.NT2017★ 6 cited

Bifurcation sets arising from non-integer base expansions

Pieter Allaart, Simon Baker, Derong Kong

Given a positive integer $M$ and $q \in (1, M + 1]$ , let $U_{q}$ be the set of $x \in [0, M / (q - 1)]$ having a unique $q$ -expansion: there exists a unique sequence $(x_i)=x_1x_2\ldot…

math.DS2017★ 6 cited

Digit frequencies and self-affine sets with non-empty interior

Simon Baker

In this paper we study digit frequencies in the setting of expansions in non-integer bases, and self-affine sets with non-empty interior. Within expansions in non-integer bases we…

Exceptional digit frequencies and expansions in non-integer bases

Numbers with simply normal β-expansions

Bifurcation sets arising from non-integer base expansions

Digit frequencies and self-affine sets with non-empty interior

Numbers with simply normal $β$ -expansions