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

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Showing 2012 · math.DSShow all

4 papers · 2 filters

math.DS2012

On universal and periodic $β$ -expansions, and the Hausdorff dimension of the set of all expansions

Simon Baker

In this paper we study the topology of a set naturally arising from the study of $β$ -expansions. After proving several elementary results for this set we study the case when our ba…

math.DS2012★ 10 cited

Generalised golden ratios over integer alphabets

Simon Baker

It is a well known result that for $β \in (1, \frac{1 + 5}{2})$ and $x \in (0, \frac{1}{β - 1})$ there exists uncountably many $(ε_{i})_{i = 1}^{\infty} \in 0, 1^{N}$ such that…

math.DS2012★ 4 cited

A multifractal zeta function for cookie cutter sets

Simon Baker

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a…

math.DS2012

The growth rate and dimension theory of beta-expansions

Simon Baker

In a recent paper of Feng and Sidorov they show that for $β \in (1, \frac{1 + 5}{2})$ the set of $β$ -expansions grows exponentially for every $x \in (0, \frac{1}{β - 1})$ . In this pap…

On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions

Generalised golden ratios over integer alphabets

A multifractal zeta function for cookie cutter sets

The growth rate and dimension theory of beta-expansions

On universal and periodic $β$ -expansions, and the Hausdorff dimension of the set of all expansions