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arXiv · 2506.01803

Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics

Jonny Imbierski·Charlene Kalle
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Abstract

In this article we derive a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets associated with non-autonomous dynamics constructed from families of countable affine iterated function systems. The formula obtained shows that the universal-lower-bound phenomenon present in the autonomous case studied by Fan et al. (2010) persists in this non-autonomous setting.

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Jonny Imbierski, Charlene Kalle. 2025-06-02. Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics. https://arxiv.org/abs/2506.01803

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