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 2014Show all

6 papers · 1 filter

math.DS2014

Dynamical properties of S-gap shifts and other shift spaces

Simon Baker, Andrei E. Ghenciu

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts…

math.NT2014★ 7 cited

On the distribution of powers of real numbers modulo 1

Simon Baker

Given a strictly increasing sequence of positive real numbers tending to infinity $(q_{n})_{n = 1}^{\infty}$ , and an arbitrary sequence of real numbers $(r_{n})_{n = 1}^{\infty} .$ We s…

math.NT2014

Approximation properties of $β$ -expansions

Simon Baker

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

math.DS2014

On univoque points for self-similar sets

Simon Baker, Karma Dajani, Kan Jiang

Let $K \subseteq R$ be the unique attractor of an iterated function system. We consider the case where $K$ is an interval and study those elements of $K$ with a unique codin…

math.NT2014

Badly approximable numbers for sequences of balls

Simon Baker

It is a classical result from Diophantine approximation that the set of badly approximable numbers has Lebesgue measure zero. In this paper we generalise this result to more genera…

math.DS2014

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Simon Baker

Let $λ_{1}, \dots, λ_{n}$ be real numbers in $(0, 1)$ and $p_{1}, \dots, p_{n}$ be points in $R^{d}$ . Consider the collection of maps $f_{j} : R^{d} \to R^{d}$ …

Dynamical properties of S-gap shifts and other shift spaces

On the distribution of powers of real numbers modulo 1

Approximation properties of β-expansions

On univoque points for self-similar sets

Badly approximable numbers for sequences of balls

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Approximation properties of $β$ -expansions