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 2021Show all

4 papers · 1 filter

math.DS2021

On normal numbers and self-similar measures

Simon Baker

In this paper we prove that if ${φ_{i} (x) = λ x + t_{i}}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $\frac{\log b}{\log |λ|}\notin\mathbb{Q},…

math.NT2021

Metric results for numbers with multiple $q$ -expansions

Simon Baker, Yuru Zou

Let $M$ be a positive integer and $q \in (1, M + 1]$ . A $q$ -expansion of a real number $x$ is a sequence $(c_{i}) = c_{1} c_{2} \dots$ with $c_{i} \in {0, 1, \dots, M}$ such that $x=\sum_{i=1}^{…

math.NT2021

Intrinsic Diophantine Approximation for overlapping iterated function systems

Simon Baker

In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine's theorem for these sets. We then appl…

math.DS2021

New dimension bounds for $α β$ sets

Simon Baker

In this paper we obtain new lower bounds for the upper box dimension of $α β$ sets. As a corollary of our main result, we show that if $α$ is not a Liouville number and $β$ is a Lio…

On normal numbers and self-similar measures

Metric results for numbers with multiple q-expansions

Intrinsic Diophantine Approximation for overlapping iterated function systems

New dimension bounds for αβ sets

Metric results for numbers with multiple $q$ -expansions

New dimension bounds for $α β$ sets