Simon Baker

A multifractal zeta function for Gibbs measures supported on cookie-cutter sets

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 new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures.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 new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures.

ON SMALL BASES FOR WHICH 1 HAS COUNTABLY MANY EXPANSIONS

Let

Unique expansions and intersections of Cantor sets

q\in(1,2)

The organosulphur cycle: aerobic and anaerobic processes leading to turnover of C1-sulphur compounds

. A

On small bases which admit countably many expansions

q

Generalised golden ratios over integer alphabets

-expansion of a number

Expansions in non-integer bases: lower order revisited

x

The growth rate and dimension theory of beta-expansions

in

On univoque points for self-similar sets

[0,\frac{1}{q-1}]

Entropy, topological transitivity, and dimensional properties of unique q-expansions

is a sequence