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arXiv · 2310.15265

Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy

Jonny Imbierski·Charlene Kalle·Reza Mohammadpour
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Abstract

In this article, we calculate the Birkhoff spectrum in terms of the Hausdorff dimension of level sets for Birkhoff averages of continuous potentials for a certain family of diagonally affine IFS's. Also, we study Besicovitch-Eggleston sets for finite GLS number systems with redundancy. The redundancy refers to the fact that each number $x \in [0,1]$ has uncountably many expansions in the system. We determine the Hausdorff dimension of digit frequency sets for such expansions along fibres.

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Jonny Imbierski, Charlene Kalle, Reza Mohammadpour. 2024-11-24. Birkhoff spectrum for diagonally self-affine sets and digit frequencies for GLS systems with redundancy. https://doi.org/10.1017/prm.2024.113

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