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 2015Show all

4 papers · 1 filter

math.NT2015

On the regularity of the generalised golden ratio function

Simon Baker, Wolfgang Steiner

Given a finite set of real numbers $A$ , the generalised golden ratio is the unique real number $G (A) > 1$ for which we only have trivial unique expansions in smaller base…

math.CA2015

Inhomogeneous self-similar sets with overlaps

Simon Baker, Jonathan M. Fraser, András Máthé

It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of th…

math.NT2015

Approximation properties of $β$ -expansions II

Simon Baker

Given $β \in (1, 2)$ and $x \in [0, \frac{1}{β - 1}]$ , a sequence $(ε_{i})_{i = 1}^{\infty} \in {0, 1}^{N}$ is called a $β$ -expansion for $x$ if $$x=\sum_{i=1}^{\infty}\frac{ε_{i}}{β…

math.NT2015★ 5 cited

On small bases for which $1$ has countably many expansions

Yuru Zou, Lijin Wang, Jian Lu +1

Let $q \in (1, 2)$ . A $q$ -expansion of a number $x$ in $[0, \frac{1}{q - 1}]$ is a sequence $(δ_{i})_{i = 1}^{\infty} \in {0, 1}^{N}$ satisfying $$ x=\sum_{i=1}^\infty\frac{δ_i}{q^i}.$…

On the regularity of the generalised golden ratio function

Inhomogeneous self-similar sets with overlaps

Approximation properties of β-expansions II

On small bases for which 1 has countably many expansions

Approximation properties of $β$ -expansions II

On small bases for which $1$ has countably many expansions