English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article we study Besicovitch-Eggleston sets for finite GLS numbersystems with redundancy. These number systems produce number expansionsreminiscent of Cantor base expansions. The redundancy refers to the fact thateach number $x \in [0,1]$ has uncountably many representations in the system.We distinguish between these representations by adding an extra dimension anddescribing the system as a diagonally affine IFS on $\mathbb R^2$. For theassociated two dimensional level sets of digit frequencies we give the Birkhoffspectrum and an expression for the Hausdorff dimension. To obtain these resultswe first prove a more general result on the Hausdorff dimension of level setsfor Birkhoff averages of continuous potentials for a certain family ofdiagonally affine IFS's. We also study the Hausdorff dimension of digitfrequency sets along fibres.

Besicovitch-Eggleston sets for finite GLS number systems with redundancy